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16.04090000 2ow . U

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ISBN 5-80840567- X

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utipbw: Pmgb Pm~fihpp utpbmjbg, wmdml/mG ppmbGb uqh~mpntb hwm-

Gmptpqmb ti6 dfi zmpp ~1 utpbmlitp, npnGp G t p 4 ~ w g q n t d t G hmdmGdmG ~mGm&Ltpnq: Ujuytiu, uqbbmpb nt~mpmdw~n12m~mqntjli dwuntd Lmjdw- dp hwjmlimqnpbtg db u t i p b ~ , npp Gllmpmqpantd t htimLjwl p m G m & b ~

UytLpq-ib bGgpmQwpdbp dmuntd qmG14wb tiG htimLjml t p t g utipbmGtpp.

Qm2 tGb '

p~@mGntp pwGm&hq, n p m h k-li m a u l uhpbmjb hmdmp hmummmntti t (k = 1, 2, 3, 4, . . .), bu4 n = k + 1, k + 2, . . .: (6) pm[iw&Lp Qn~qn~rF t P m ~ d t p b pGrlhmGpmgqwb FWQW&L:

iL$tlnq hmnwqwjpfimfi 1* blmGdmG pqmlimqbG pGn~jpb durubG

rrllmfihb dmp4wbbg, L. Pnpp dt4GwpmGhg ppmbGb L ppmbGmGdmG mmdGhpb uqti4mpmj~G op~tiwym~n~pjnttifihpp:

Cum Pnpb, mmndntd t~tllmpnGp Qurpnq t qmmqt l dbtqG npn2mbb ummglmlimp n ~ q t b p b p q , npGg hmdmp pmqmpmp~ntd t htimLjml qmjdmGp, npp bntqntd t Pnpb p~mGmmgdmG ymjdmG.

npmtq p, -6 tltbmpnGb )dyntlub dndtGmb d q y G t , m-p' tlti~mpnlib

qmGqqmbp, r-p' p.unwm-dtQmnpb dntptlp, 4 -p' qmmdmli w G ~ n t G q b G

mpmqn~pjn~Gp, n = 1,2,3, . . ., h-p' 'QlrnGQ hmumwm~Gp, A = h / 2 ~ : Cpp-

pluGmjbG mqtb-pp hmdmp p, = mva , npmtrla-6 2~9mGu~qbb 2wnmWG t :

flpn2tGp ummg@iGmp nultbpbpb 2mnmmG bpG 111 m m d b u1bq tGtp@uG ypmbGm GdmG mmndlihpn~d:

U m d b ~ 1 p q tGtpqbmG hm~mump t tlt4mpnGb L dbpn tu *n- ~mqqtigntpjmG qnmtGg~m1 L tlt\mpnGb QGtmb4 tGlipc@~Ghpb qntdmpbG (hlipmqpqntd t, np dbpnt4G mG2mpd t): t1t4mpnGb bGtimb4 tGtp&mG bnpn~tGp Ljnt~nnGb I1 optGpbg, npmtq d b p n ~ ~ L tlh4mpnGb a n - ~mqgtigntpjwti Qn~lnG~md nt* 4mmwpnd t bbGmpGm&bq ntdb qbp'

z e 2 mu2 -=- mv2 .Ze2 - 4wd ---: a2 a 2 2a (8)

Q p n ~ b L tltbmpnlib @nNwqqtgn~pjm qnmtiligbml tGtipc~~mG'

(8) L (9) urpmmhmjm~p~ntGGhppg mmndb ~ 1 b q tGtrp~j~mjb hmdmp ~ummGmGp.

<m21& mnGhlnq (8) L (10) pmGw&1*tipp L Pnpb pqmGmwgdmG (7) ymj- dmGp, ummgklimp nqlibptpb 2mnmlllqGtipb L ummglmGmp @hm4Gbpb tGhp@mGhpb mpdhpGhpb hmdmp hmdmqmmmu~mGmpmp ~umurGmGp.

npb mpdhpp 2mm dnm t (1) pmGm&Ln~d wn4m ~ p & m n m ~ m G mpdbpbG, bG>p hmummmntd t ppmbGmGdmG mmndGhpb hmdmp qmpqmgqmb Pnpb UIhunlpj~G h~6mp~nmg@tpjn~Gp:

fipm4wGntb fi&bpc& hmumurmtGb mpdhpp 2wm mqho dnm t $mp&mnmQmG mpdhpbG: PmGG LUJG t, np (12) L (14) pmGmdLtipG wp-

mmbhlhu t if iamwqh~ t , np dbpnl4G mfi2mpd t : U]lpntL& ~ m p c h d p hm2@ mnGhlnt hmdmp wGhpmdh2m t t~t4mpnGb qmGqqmbp @ni-umpbGtl Gpm

phpawb qmfiqdwhq' m, = mM/(m + M ) , npmhq M-p dbyn~llfi qmGqJmbG

npp dbb 6 ~ ~ n n l ~ ~ m d p hmd.pGQGn~d t @np&nq npn2qmb mpdhpb hhm:

Uju m2FmmmGpp G@pqmb t ppmbGb mmndmlpG uqb4mpb Pmldtph ubppmjb nlun~dGmubpn~p~mGp: L ~ q w b uhpbmjb uqb4mpmj~G qbtpb m&p- Ghpb tiplppn~pjntGGhp pmqmpmpn~d hG (1) LUntip~pjLUGp:

U2~wmluGpt1 Gqlumw4p Uju m2lummmGpb G y m m m ~ G t.

I . n p n ~ h ~ ypmblib mmndb uyh4mpn1d Ha, Hp, H, qbbpbG limdmqm-

mmu~mGnq m@pGhpb trp~mpntpjntGGtipp:

2. UdhG db m&b t i p t p ~ p n ~ p j ~ ~ f i p hmdmu~mmuru~mGhgGh~ bp n mdpnqp

abqe: 3. <m2qtl fi&hp@ hmummm~Gp' oqm$ilnq npn2qub m&pGhpb tp4m-

pn~pjn~GGbpbg L wmGg hmdmqmmmu~mGnq n mdpnqp pqtpbg:

q. bmnntghl mfipb hpljmpnlpjmli L pdpntw gntghtGgb dbpL ljwludmG wm4bljp' @ Y ~ P U ~ J ~ G l j n ~ ~ , hm241 mnGh~nq, np uG*U u ~ b l j m p b mnwqh~ bGmtrGubq uyhljmpmj~G qbhpbG hmdwywmmu~mGntd hG w-

htmhjml hp4mpntpjntGlihpp' 6907i , 5790,7.i, 5769,6i, 5460,7i,

4916 i , 4358,3i, 4046i : 2.9pcubGb umndb u~qti4mpcuj~fi q&bpb cu~bgb bp4wpn~pjn~GGbpb n p n 2 n ~ d ~

m. YM-2 umppb nb~ub $pm mliqmrlpbl ppwbGb ~ m d y p dntmgb filiqg,Ig

L > 4F hhmqnpn~pjul i $pw (F-p ljnGqhGunpqjiG n u y G j w ~ bbqw-

hhmwjbfi hhnmqnpntpjntEG t):

p. bnGqbGunpqbG nuyGjml& oqGnIpjmdp [ m d a ~n tumpdm~nq dmqm-

Gnpb ulwm4hpp ul fm~tl jmb~ b u w b d b b g w n w wqw tbwGbG, mjGnthhmL t4pmGp hhnmgdhl:

q. Qpwnbl wum~hwGmj~G p d p n t b wdhG db qbbG hmdmymmmu~mGnq gntgdntGpp:

q. ?-buyl ipu~bG Qnpb oqGnlpjmdp npn2b~ ppmbGb mmndp uyt4mpwjb(i

q b b b w Lkb ~ P ~ u ~ I ~ V J ~ ~ G G ~ P Q : 3. flbqptipqb huumwmn~Gb n p n 2 n ~ d ~ U@pb hp4mpntpjwG jntpmpmfi~nlp qmlidwb mpdhpb L q w l i hmdm-

ymmwupmGnq n pfi oqGntpjmdp (1) pmGmbLnq hw2qhl f i m h p q l ~ hwu-

mmmntGp: UhpbmkmG o p ~ E m ~ m ~ t p j m G 6~dmpmmg~1pjmG hwmmGb2 t tnunwntd mmpb mmpphp tip4mpntp~nrGGbp~ hmdmp umwg@.ub R-p

wpctlipGhpb hwdpG4Gntdp:

u s n t ~ n ~ u ~ u ~ qurstr 1. haGy t ~Lqh~U'IpwjbG ulipbmG L bG2@uba ulip~wGIip DG a m q n t d

ppmbEmGdwG mmdGhpb uyhljmptd: 2. napG t Pnpb g~mGmmgdwG y q d m G p 2pymGuJbG nultibphpb hwdwp:

3. hG$' t hmqmump ppmbGwGdmG wmd, I n-pq ummglmGmp nullibpp

~ m n m m p L m m d f i tGhp&wG, bpp tlhQmpnGp qmmqntd t mjq ntqbbpnq:

4. bGpqtiau t ummgqntd Pmldbpb pGqhmGpmgqwb u h p ~ m j b pmGw&Lp: 5. bG2yhau t npn2qntd f i h h p a hmummmntGb mtuwljmG mpbbpp:

StUULtUL UUU

I. U~PPUQUL ~ u n n ~ ~ r l u a ~ ~ ntuntnuutmtuc P n ~ n p mlljmfimQmE dhmmqGhpb /mpjmtd (Li), Gmmplmtd (Na), ljmfi-

ntd (K), n n t p w t d (Rb) L gh@~d (Cs) / wmdmljmG uyh~mplihpp 2mm

6dmG ti6 hpmp L hmdhdmmmpmp ympq mtiug ntGhG: Ujq uyt~mpGhpp GmL npn2 GdwGntpjntG ntGhG ppwbGb m m d b uyti4mpbG: Oqmqtilnq u j q GdwGntpjntlifig' fifqphpqG w~ljw@mllmG dhmmqGbpb uytljmpwjbG qbhpp IintjGqhu ludpmqnptl t pum mnmG&bG uhpbmGhpr rlpmGp Ghp4~wgEhlnq htimhjml ljhpI.4.

npmtiq v'= 1//2 dhbmpjntEp mQml qbb mfipujbfi pb.@ t, R-P' f i h . F h ~ @

hwummmn~Gp, s-p, p-G L d-G m a w 1 dhmwrl(p hmdmp hmumwmtG L dhWg $npp pqhp hG: s << 1 L p << 1 qtiqgntd q&mdnp uhpbmG hwdpGhGntd t ppmb6b mmndp LuqdmGb uhpbmjh hhm:

OnpClbpp gnljg hG mm@u, np wlljmfimljwG dbmwrl(p m m n d m 4 ~ 6 uulb4~pmjbG qbbpp hwGqhu hG qmfiu qntjqhpnq 1U14GullGhpnq, f i h ~ h p q b (1) pmGm&Lhpp qpqmb ti6 qnyq qbtipbg d b w hmdmp: U J ~ ~ ~ G ~ & L h p p dh4GmpmGhln1 hmdmp mGhpmcth2m t npnzhl mlljmIlm$Pfi

dtmm* m m d b tG€ip@mG mmpptp m6mQGtpntd L, oqmqhlnq hmhwwt- pjntGGtpb dmubG Enpb QmCi-umqpntjpbg, npn2tl mQml utpbmjb mGgntd-

GlipbG hmdmymmmu~mGnq gnmnlilitrpb tGtpqbmGtpp' h v = En - Ek , npmtiq En-p n-pq (qhpbG), hu4 E k - G ' k-pq (umnpbG) dw~mpqw4Gtpb tGtp-

@mGtpG tG: UmljwjG Pnpb mtun~pjmdp ml~wfim4mG dtimm* mmndb tGbp@wG 6.p41bm npnztil hGmpmqnp rt:

Uju m ~ ~ m m m G p n t d mpqmb t luGqpb np~uQm4mG pGGmpl.prdp, bu4 pmGm4m4mG mpq~nrGpGtp ummGmlnt hmdmp oqmqntd tGp @p&ntd ummg~mb mawlGtpbg:

Onpcthpp gnyg t G mmfllu, np ml~mfiw4mG dhmm* mmndbg d t 4 tlt4mpnG htnmgGtlnt hmdmp ymhmlipqnq tGtpqbmG (wmpbG @GmgdmG tGtp@m) ~ w m mGqmd @pp t Lu dli4 t~IiQmpnG htnmglililn~ hmdmp mGhpmdti2m tGtp@mjbg (bptpnpq ~ G m g d m G tGtpQm): UjubGpG' db tltLlmpnGp 2mm mqtifi htinnr t dbpnrug, pmG dGmgmb tltllmpnGGtpp:

Ujuu.&unq, Z Qmpqmpbq mGtignq mllpufimlpuG dtrmmr& w m d p 4m-

pbfi t ymm4tpmgGtrl h tmljml Qtipy: Umnbb (Z - 1 ) tltlp.npnGGtpp ~ m m

Imm t G dbpntuG (npb figpp +Ze t ) L qtppbGbu htrm dbmubG hmqdntd t G +e figs n~Gtgnq db md*n* hmdm~mpq, npp Qnlqnrd t mmdmQmG hbdp: bu4

6b tlt4mpnGp htnnt t dbpntQg: Ujq tlt4mpnGp Qntqn~d t oqmb4m~mG,

npmtq n-p q&wqnp p~mGmmj~G pPqG t : QNmqnp pqmGmmjbG p U d t b

mpdtgGhpb qtqpntd tltlpnpnGp hmdtdmmmpmp htnnr t qmGqntd mmn-

dm4mG hbdpbg, L (2) ~ m f i ~ d h 2 PW~"JPV t i 2 m t p ~ ~ ~ l d ~ 11uphfi t Upmnhl w L g u l f i ~ Q ~ G d t m m ~ wmndb hmdmp:

UmllwG qmmqnp pqmGmwb6 pLUl hmdtdmmmpmp gnpp mpdtpGtpb $iqpntd mlQw@mQmG f ihmma m m d b tGtp@wG m~~pphpqnrd t ppmbGb

mmndb tGtrpaw~bg thp4nr ~ w m 6 m n n q : PmGG mjG t, np oymb4m4mG tlti4mpnGb tlii~mpm4mG qm2mG mnw-

pmgGn~d t mmndmllmfi hbdpb pltnmgnrd, qupGpG' umt iqh~d t qhynlmjbfi dndtGm, npb ntqqntpjnrGG tlt4mpnGb ~mp&mGp qntqpGpmg mGpGqhmm

*n@nlullntd t : tlli4mpnGb wnmtGgbwl tGlip@mG mpqtG lpnmpptpa

ppmbGb mmndnrd tlthmpnGb ynmhGgbml tGtp@qbg, gmGb np, pmgb

hbdpb htim IlntlnG~v~G *nbmqqbgmpjnrGbg, tltQmpnGp GmL q q *qnm wqqhgnt~lnr Gp:

Ujntu Onqdbg, mqbdntmmjbG pqmGmmjbG p a w p p mpdtpGtpb qtulpnrd t f i y m ~ 4 ~ G ' ~ n q b b p t p p p m ~ m ~ m G m ~ m @ , 1. utqdqmb tG, ntumb Lppnq l i G pm$mGgtl ~mndm4mG hbdpb mbpnqp:

-bjmGb t , np tfiymm4wG nqtbphpb a L b ~umnmGgpGtpp npnzqntd

bo n q m ~ l l n p ~ W G ~ W J ~ G p U L n, m@dntmmjuJPG pqLU6LnLUjb6 p m mpd.tpGtpnq'

npmtq a, = h2/rne2 = 0,53 lo-* ud hmummmrGp ppmbGb mmndb mnm-

~ b f i nulbbpb 2 ~ ~ r n G t (Pnpb 2wnuJW): LmpLnp t G 2 t ~ np n,-b mmpptp mpdtpGtpb hmdmp ntqtibDlipF m m -

dmLpuG hbdpb mbpnyp pm~mGgdmG mumbhuGGbpp mmppbp IlfiGhG, npb qmmhmnnq tl mmpptp 4 f i G t E m l ~ m f i m ~ m G dhmmqj m m d b tGtpr&mGtr- pp, mjuhGg G' 4qtipmGm u~~puhpnrdG Cum m@dntmujbG pqmGmwjb6 p a :

Ujuuunq , mlQm~mlpuG dtmm* mmndb tGhp@m~mG uqbgmpp (mnmGg mmndm~m6 hpdpb tGtp&wb) bmptfi t Gtipbm~mgfit~

~mGm&Lnq, npmtq A(n,) dlibntpjntlip Qnlqntd t p~wGmwj'pG nqqntd L

k w b q u ~ b t abmjG n, -bg: n,-b d t b wpdtpGtpb q t w m d A(n,) -+ 0, L (4)

pmGw&Lp hmdpGllGn~d t ppmbGb m w d b tGhpqlIwllmG uyhQmpb (2) pmGmdLb hhm:

n q@mqnp pqmGmqbG pqnq npnzqn~d t dbwjG oulmhllwllmli tltillmpnGnq y ~ d m l i u q n p q u t b tGtipqlImQm6 dJ6mQp: S a m [ mllpufimlpG d t m m u mmndb hmdmp n-b mdtilim@n~p mpcfhpp hmdmymmmu~mGn~d t hbdGmkm6 ( m q n W b ) WmllbG, ~ m f i b np qpmGbg @ ~ P P ~4mDmwbG pqhpnq pnlnp Q6m4Gtipp ~ l w g q m b hG dGwgmb tlh4mpnGGhpnq: Ujuqtiu,

opbGw4, Li-b mmndb hmdwp nmin = 2, Na-b m w d b hwdmp nmin = 3, K-P wmndb hmdmp n,,, = 4 L LLIJLG:

A@,)-G np2dntd t ~ p & G m l p ~ G bqmGmtpq:

<b~hGp, np pnlnp n, = 1 #6wQGbpp 4n>qnd hG s 9 6 m ~ G b p , n, = 2' p 1 I

I@UldwbGtp, n,= 3' d I@Uldm4Gtrp, n, = 4' f ~ b m 4 G t p L wj~G: Pnlnp wlhm- Dm4mG dtmmrlGtipb 1qpcpqmb mmndGtpb oym)4wQmG tlh~mpnGGtpp ' qmGqntd hG s dJ6mQntLl (n,= 1 ) : PGI~LGI@I~ t s mmnbg mnmp qptq q@w-

qnp pqmGmuqbG p a mpcfhpp: Ujuyhu, Na-li2qpqnqmb mwdnud oymblpu-

QwG tlii4mpnGb hmdmp n = 3, n, = I , ntumb UJJG qmGqntd t 3s Q6m4ntd:

bt u ~ p b f i 4hfiwM s@mdnp ~Wfimu?lllG PMP fi2~uGmlltG~ k-rill, w y m k h nv= 1 pqmGmmjpG pqtrpnq npn2qnq (Ilp6mm' ks) mbmlpul:

qmGqnq m m d l i tGhpqfimG'

me4 1 Eks = -- - 2h2 ( k - A , ) ~ '

(5)

Q@urqnp utpfImjb uqti4mpurj)G qbtipG mnmpmGnrd hG, tipp m m d n t d

np @tSwLptd qmGqnq oymbllmlpG tlhllmpnGG mGgGn~d t mdbGmgmQ~ ks

@rim4 (G4.12): Ujq mGgdmG qt iwntd 6 m n m q ~ p q w b 4nmnGb tGhp@mG' r 7

(7), (8) L (9) pmGm&Llipp 4hmdpGbGhG B m h p q l ~ (1) ~uGmhLtip) hbm,

hph, opbGm4, Na-b hmdwp pGqntGtGp, np 1 + s = 3 - A,, 2 + p = 3 - Ap h

n + d = n - A d :

U~4mfim\luG dtmmqGtpb @Giytu GmL prilnp mmpplipb) w~l~lLlmlluG uyhQmpGhpn~d fimantd t htrmhjwl ummG&GmhLumQntpjnt~pP uyhl/mpntd Qmqntd t l i ~ ~ ~ L u J G LUJG qbtipp, L U J U ~ G ~ G ' p n ~ j ~ m m p h ~ hli dhmj6 ~ J G

wGgn~dGhpp, npnGg qhypntd m@dntmmjhG p4mGmw~hG P P ~ P W b q n ~ a t dh4nq, LUjubGpG' h v = + l : Uju y ~ r p t d p hntqntd t pn4dmG Qu3Gnfi b

hm~mGmphp$i~ t +np&Gm@G 6mGmymphn~: <tmmqwJntd pn4dmG 4 ~ - GnGbfi mpqhl t mtiumlp~~G dbQGmpmOntd:

2. U"lbL-llt'LtbPU3bL o n ~ u ~ ~ t ~ n t t a 3 u ~ wuqusntuc

FG>ytu mpqtG G~qbl t, m ~ l / m ~ m 4 m G dtmwqlihpb pnlnp uyb~mpmjbl i qbtpp hmGqtu hG qmfiu qnyqtpnq tpl$~uQGtpnq ( t p 4 n ~ ' bpmp Zmm dnm qmumqnpqmb qbbp):

Ujq q n ~ q t p b hmdmp *mqntd t G htmLjml opbGm>m+n~pjn~GGtipp.

1. Q f i ~ l l n ~ ubpbu?lb qbtpb q n ~ ~ q b m f i ~ m ~ b f i A t p b ~ ~ ~ F ~ P L P J ~ ~ G G mdtdmdtbd t unmpbG q n y a hmdmp L qfimqnp pqmGmwjbG pbqp dbbmglitfiu mjG mumb6mGmpup +nppmGntd t:

2. UnmpbG h tplipnpq ~ n q d l i m ~ utpbmGtpb hwdmp mjq mmppti- pnlpjntbp h m u m m m ~ G t L huqmump t qfimqnp ~ ~ b p b m j b mnmybti qntjqb

~ f i ~ u ~ ~ b G B ' I ~ P ~ m w p p t p n l ~ ~ m f i p : U ~ t h m p m ~ b G qbhpb q n l ~ q t p b W J ~ ~ P J J ~ L ~ ~ T ? ~ ~ ~ d m G ~ q n ~ ~ ~ t ~ P W P

2mm dnm tpljnl t C t p ~ m ~ m G @6mQGtpl1 qnjnlpjmdp, bud , b(i)ultu pGqn~Gqmb t m u t ~ tGtp@mQmL @6mQGtpb 6tqp/mbn~pjwdp:

UlQmfimlpuG dbmmqGtpb u t q t 4 m p m ~ ~ G qbtpb ~pljG~4mGntpjntGp, 4md, np GnljliG t , tGtp@m@mG @fiu4Gtpb 6tiqpqmbntpjn1Gp pmgmmptlnt

hmdmp fltltGptr4G n~ Q~un~qufibpC wnmpmpl$tgfiG db qmpllmb, hmdm&mjG npb t l t~mpnl i l i m611 ut i@m~uG dtbmGb4m4mG L dmqG~um4mG

dndtGmGtp: Ut+m4mG d t ~ m G ~ 4 m 4 m G dndtLmG mGqmGtgfiG u ~ G : tqlitlnq mjG J?mumbg, np mwdnud ntqhbpwjbd dtbwGb4m4mG L

dmqdbumlpud dndtGmGtpb dbhtpjn~GGtpp p~mGmmg$ub tG, mj-

ubQgC' p, = n,h L p, = n,p, ( p, = eA/2rnc h m u m m u ~ l i p Pnpb dmqdli-

w G G t), u h ~ m ~ m G dndtiGmGtppG Gn~jGqtu qtpmqptgbG pqmlimmgqmb

UIpdtpfibJl, Ulj~bGpfi' p, = sh h ,Us = Upo :

s-G mL@AitgbG u a C w j b C pqwGmqbG p11q: <tmmqmjn~d (opbGm4'

CmtnGb L Qtn lmbb +np&bg) qmpqqtg, np a= 2s : t G t p a m l p u 6 #fiwljlitpb 6hqpn1dG ntltGptl$i nt 4-mn~qudbpp pm-

gmmptgbli hhmLjml Ijhpy: &mGb np t~t4mpnGd ntdb ut1@m4mfi d t -

~mdbllmLlmG dndtGm, m u p W E nqtbpu?)bG dndtGmGtp~ Li~LUmdLLIdp

4ntGtGm npn2mw q u u r n ~ n p ~ m b n t p j n t ~ : SQml q w u m q n p q m b n ~ p j ~ q h y -

gntd ut+m4mG dmqGpum4mG dndtdmb L H p n~qtbpmjbli d m q G ~ u m ~ m G

pufiur&Lnd, npmtq 8,.-p ut+m4mG dmqGbum4~~G dndtGmb L nqtbpmjbG

qm2mb dllpL 4mqd~@b mGllln~GC t : b ~ [ i b ~ n ' I W G J?mumbg, np m l ~ m f i m t p t i

dtmmqdtpntd uu&G-nqtbpmj1lG Lbnlumqqhgn~pjmG tGtpqbmG pGqn~Gntd t dpmjG tp4n1 mpdhg (qbbpp tpljntuli LC), 8, mGQjn1I6 n~Gb dbmjd t p k m

~ p d t p : ~2mGp np h m ~ m u m p m 4 2 ~ @6m4Ghpntd 8, = 0 Qmd 0, = n, ntptdd

ntqtbpb G4mmdmdp 4mpnq t qmumqnpqtl dpmjG q n ~ q m h t n 4md

hm~wqntqwhbn:

Uybhmpm~bG 9bb ~ f i ~ b ~ P ~ ~ P L F J ~ ~ G P npn2qntd t hp4nt LUl6~4Gtpb ($tipbG L umnpbG) tdbp@mGtpb mLUpph~lpjLUdp, L tipt 6 t i l u q ~ b fiGhb6

Fnlnp WmllGtpp, M Y ~ u ~ h 4 m p m ~ b G q b t ~ b p b d ~ 4fiGtp tp4n~ubg mdtf i : bG>ybu G ~ q t g , q@mqnp utpbmjb uyh4mpmj~G qbtpG mnmpmGn1d tG, tpp

m m d n t d np @hu14ntd qmGqnq oqmplp4mG tlt4mpnGG mGgGntd t wdtfiwgmtq ki @6m4: n t~ tGptQp L Qmnqudbpp umbqqmb. tqmG pG-

qntGti~ np s U6m4Ghpp >liG 6 h 1 ~ q n t d , mjub6pG' s @6m4Gtpntd nqhbpmjbG

q m p p L dndtGmGhpp pmgmljmjnud hG: %pm hmdmp n, m@dnumm~bd

Ut@m4mG L n q t b p m j ~ G dndtEmGhpb qmqmhtn 4md hm4mqntqmhh qumu'InpntpjntC nditgnq @hmLGtpp 4mmppbpqtfi bpmpbg n> ~ ~ W J G t f i t ~ a m ~ n q , mjlL @bq ( q n ~ d m p q b G ) dndtlimnq, npp n> bbum ~llmGmwlbG

dnmbgdurdp 4mptf i t Ghp@j~gfibl j = p , + p s mtupnq, bu4 vbq dndtfi-

mbG ~ ~ ~ u I u ~ u I ~ u I u ~ ~ G ~ p~mGmmj]~G pbqp, npp 4nlqntd t GtpgbG

pqwGmmjbG pbq, j = 1 + s mbupnd: UtrQ oymb4wQmG tlti4mpnli ympn~Gw-

411~1 mmndGhpb hmdmp j = 1 f 112, pmgb s @6wQGhpbg, npmhq j = 112 :

U J ~ LUl6wllGtpG b p ~ p b g m ~ p p t p b ~ n l hmdwp 4WmW W p h m ~ G b 2 b ( m w b ) GtppLb mp wG4_lntGntd qpdntd t GbppbG pqmlimmjbG p# mpdlipp: Ujuyhu, opbGmQ, 4Pw2 G2mGmQntd t' n = 4, 1 = 1, j = 3/2 (qntqmhtn

qmuwqnpqmbntpjntG): 4PIl2 G2mGmQn~d t' n = 4, 1 = 1, j = 1/2 (hmQm-

qntqmhlin qmuwqnpflmbn~pjn~G): C[iqhmGpntpjnlGp .$wbmhlnt hmdmp 112 t qpqntd Gwh s @hwQGlipb hmilwp: LQ.12-mil pbpqmb t Gmmp@tntdb m m d b

hGwpwqnp tGhpc$wQmG *hmllGtrpfi ubhdmG qfimqnp p~mGmmjbG p#

n l 10 mpdhpGbplp hmdwp: qbdmQGhpp ymm4hp~mb hG hnpbqnGmQmC

4 ~ ~ 6 qmpnll, npnGg 4 w b G q q m b t Wphpr~uGb2p: qb6mW tfihps]luG n ~ 2 q n l f i t 9bb d W n q nulrlm&q nulr lnV~md~ (GbwPn~d dv*u2mw~p Lb ymhymliqmb): Lwmp@tdb m u d p oymbQmQmG tltlpnpnlib mdtGwgwbp

tGhpc&wQwG t&dmQp 3Sln miiwQG t , npp Qntqntd t hbdGmQwG: Ulimgmb

pnlnp @dmQGhpp Qnrqn~d hG qpqndwb: Ubhdmjntd G2qmb t G pnQfimG QmGnGnd pnnylmmp~nq wGgntdGhpp L qpwGg h m d u r y m m w u ~ m G ~ mopb

tp4rnp~pjntGfitpp (php qbtip): Ubtdmjntil d @bmQGhpb dbrpn~dp hm2@ ib mnGqulb, pwGb np wjq @6mQGhptd uyl~G-ntqGQ-~wjl'~G @i-uwqqhgn~pjwG tGtips]lwli Zmm @pp t:

%fYwqnp uhpbw~b L L p W m QnrldGmW uhpbwfibpfi @hpb 4~4f iw- ~ m l i n ~ p j n ~ t i p ymjdw6mqnpqmIb t dbwjli p ~&CimQGbpb hliqpnudnq: PmGb np

bp4pnpq QnqdGmw uhpbmjb qbhpG mnmpwGntd iiE, hpp tltQmpnGp npLt ns

@6mWg wGglintd t mdtlimgwbp kp QdmQ, m y w q q IlpQGmQGhpp

qmjdmGmqnpqwb Q@GhG dbmjG kp @bww bbrpntdnq L pnpp MhGmQ-

Ghpb hmdmp mfipwjfiG pqtpb m m p ~ t p n ~ p j n ~ l i p l,l@Clj~ GnyGp: Q&mqnp

u h p b q b QpQGm4GhpG mnwpmGntd hG mmpphp p @dmQGhpb Cihq~dwG

htimLwGpn4: UmllqG wdhlimdhb 6bqpntd wnwpmGntd t mdhGmgmbp p @Simllntd, pwlib np nultbpmjb[i qm2mG wjq #dmQntd wdtGurdhbG t: Ujq

v ~ ~ ~ n n d tl q@wqnp ubpbw~b unmphfi b ~ 4 f i ~ W m@pu?lbG Nbpb Lnmpptipntpjn~GG mdtiGmdhbG t:

QGmhmmhGp uUG-nqbbpwbG anbwqqbgntpjmG tGbpqbwG ppub- GmGdwG mmndGbpb hmdmp: l-lim hmdmp mGgGbGp W G Qnn~Gmmm4mG hmdm~mpqp6, npmtq tlb~mpnGG mG2mpd t, butj dbpntbp ymmqntd t Gpw

Zntppp (64.13): QpnrQb ymntjmnq yqdmGwqnpqmb I 2ppmGwjbG

hnumGpb dwqG~umlp~G q w ~ m p '

npmtq c-G p y u b mpmqn~pjntGG t qmQnm~htd , an-p' tlb4mpnGp n-pq

nqbbpb p.unmmp' a, =h2n2/rnze2 : Ze @gpnq d b p n t u umtqbmb hn-

umGpb I = Ze/Tn mpmmhmjmntpjntGp (Tn -p n-pq nulbbpnq t~b\lmpnGb

qmmdwG ymppbpn~pjntGG t ) mbqmqptilnq (1 1) pmGmdLnttl L oqmqblnq

t~bllmpnGb bdqn tpb dndtiGmb pqmGmwgdmG ma:@, = nA q ~ d m G p g ,

\lummGmGp'

npmiiq n = e2/hc 1/137 = 7,2973.10" d b h t p ~ n ~ G p bniqntd t umG-

ntqtbpmjbG @nbWrlhgn~~J"J f i 4md Gntpp bunntgqwbpb hmummmntG: ~QG-nwhbpm~bG *nb"Jq9bgn~pjmG hmzqmndmdp tGhp@mjb

6 2 ~ b m mpmwhujmnlpjntG ppmbGmGdmG wmdGhpb hmdmp ummgtl t q. q+pmL@: UjG ntGb hbmLjul mbupp.

( Z = 5 5 ) hmdmp Qmqdntd bG, hmdmymmmu~mGmpmp, 6 1,148 1 L 423 A:

2n Ze Zew, Zeh n H , =- - . = - - . - .

3 ' can T, can cm a,,

I p~pjntGGhpp: (10) p ~ b ~ f i h t d mtquqph~nq cos 8, = k1, p , = p, = eh/2mc, bfilulbu 2. n p n z b ~ q q qbbpb u tp~uQmG qum4mGh~n~p~ntGp:

GmL -f& -b hmdmp ummgqmb (12) pmGwdLp, 4ummGmGp uUG-nqbQmjbG

eh Zenh - rnz2e4 z2 asO a 3' 2rnc cma; 2h2n2 n

(13)

UCtuuSULPt'~uSUfuulJ4Uf4c

hJfiMv 1. 1. YM-2 dtGtpwGq>b dntmpb htiqpp ~ntumqnpt~ uGqb4qfiG pub@

ln~junq, mjlinthhml, oqmqtilnq uG&l& u q t ~ u p b tiplwgnq qbtpb hwjmfib w$pGtpb LipLp~pntpjn~GGtpbg, wump6wGwqnptl dtlitpwGq&

p d p n ~ u gn~gdn~GpGhpp L ly.unntgt~ &uqtpuwjbG 4npp:

2. YM-2 dtGlipwGqfi 6tqpp ~n~umi[nptl Gwrnpwldb l w d Q lnyunq L

& u ~ h ~ u u ? l b f i 4npb oqf in t~~wdp nPn2hl Gwrnpb~fib u ~ t h m p b PnlW

hphwgnrl qbtpb whpfitpb tpllwpn~~~nlGGhpe: 3. Oqmqtlnq G w u p ~ t d b m u d b tGtpqbw~wG L@6w~Gtpb u b h d q b g

(611.12)' npn~hl wjq qbtpb utipbwlpdi ywm~mGtlntpjn1Gp L qmuqnp pqwGmqbG pqtpb hmdwymmmu@wG wpdtpGtpp:

4. Oqmqtlnq (7) L (9) pwGm&Ltipbg L tlGtilnq q&mdnp utipbgb cunwpbli

9bb (k = 3, n = 3) tp@Pl bnrldfiwl& utpbwjb t p k P P l qbb (k = 3, n = 5)' Wp&ntd ~w+qwb wfipb h p \ ~ ~ p l p j ~ ~ G wp&tpGtpbg' npn~hl s L

p ~ @ h w ~ D t p b pqmGmqbG nqqn~dlitipp:

5. Oqmqhlnq (8) pwGwdLbg L mnmpbli 4qdGwlll1 utpfiwjb b p w ~ qbb

(k= 3, n =4)' Wpdntd >w@qwb mfipb tp1p~1pn1pjm6bg' npn2tl d a6wQGtipb pqwGmw~bG nqrln~dp:

6. < m ~ a wnlitlnq, np Na-I! w m d b wnwpbG ~GmgdwG tGtpc$wG'

E, = 5,1 tr l , n p n ~ t l A, pqwGmq)G nqqn~dp' oqmqtlnq

me4 1 E =-- ns 2h2 ( n - A , ) ~

plUGLll&Lllg:

hJfiqtV 2- Oqmqtlnq AE = hc/& - hc/;l, pwGudLbg, npu tq A,-p L &-p Qp4Gw-

L@G ulwml/wGnq qbtipb w h b tp4mpntpjn~GGtpG tD, hui2qwp4til uGG-

nqt&pwjbG @nl~.~wqqtgn~pjwG tGtp&wG L wjG hwdtdwmt~ (13) pw- Gm&Lbg h t r n h q mtumljwG wpqn~Gpb h t u :

1, baG> utpbwGtp t G @uqntd wltpfiwllwli dbmmqGtpb uytQmpntd L qwGp bPG> GdwGntp~ntG nlGtG ppwbGb w m d b utipbwlibpb htm:

1 2. paG> @wumhpbg L qwuqntpjntGGtrppg b~Gtlnq w~QwfiwQwG dtuulqJ

w m d p 4wpt@ t GdmGtg Ghl ppmbGb wmndbli:

3. baG> ywmhwnGtpn~ t U I ~ @ I @ ~ ~ L I I G dt imwa wmndb tGhp&wG uwp- ptpqntd ppwbGb w w d b tBtpqlIwjbg:

4, baG> pwGwdLn4 t Gtrpl/wjwg~ntd ml~wfim4mG dtmwqb w m d b tGtp-

qlIurLpuG uqtompp, baG2 t pqwGmmjbG nqqnldp L bG>nra t wjG 4ulbqLUb Ul~dIltUlUl~b(i ~ q ~ 6 L I l q b 6 pL@g:

5 . Pwgwmptl wjpuuhpdwG qtpwgntdp: 6. nap pqwQmqbG mGgn1dGtpnq ti6 ytujdmlimqnpqrnb qmwqnp, wnw-

pbG L t p w p q QqdGmI& utpbwGtpp uqtlpnpqbG qbtpp: Sh4dwG bG>ulfiubn QmGnG mtr@ ntGb w q wGgn~dGtipb hwdwp:

7. bn[i>ytu t G npn2qntd pqmlimwjbli ntqqntdGtipp s, p L d ahwbGtipb

hwdwp: 8. bnG> op~fiw~w@n~p~ntGdtip t G amqntd wl11wfimQwG d h m w qmw-

qnp L LpqdGw@ uhpbulitpp uutyt4mp~fiG qbhpb lp4Liwl.@tipb hwdwp: 9. bGp~"d t 4 u ~ w G n ~ d fltltifiptu L Qwnqudfipb qwphmiq: baG> @n-

~wqqtgn1pjwG htuLwGp t tGtp&m~wG ~J~fiwllGtpb hhqgntdp:

10. bG>yt0u t hbdlimqnpqntd s L@CimL$itipfi htqpqwb >@Gtm L nqt&pujbG

p q ~ l i U l ~ j b l i p@ wGhpwct€i2mn~p~ntGp:

'1. boa> t G ~ P P ~ G pqwfium~bfi P b d ~ , @L rnphPWGb2~, Pw- gwmptl uwpptp uhpbwfitpb 4p4Gw4Gtpb' @npdnq @nllwb opb- ~m>wI$ntpjn~GGtp~:

12. bnG~ q m ~ n ~ p j n l ~ d t p ~ g tlGtlnq L p p t o t qliwhwmt~ uGG-

nqtbpujbG I$nbmqqhgnlpj~G tGbp&~fi: 13. bG>ultnu 4mpt@ t ~pnpbGw4wGnptG npn2bl uu@G-ntrltbpw~bG @n-

hmqqhgntpjwG tGtpqbwG:

StUU4UlJ UUU

I. usnub ~ t ~ s n r u ~ u ~ u n ~ t ~ c < t m t d b m m d p Qmqdqmb t +2e @gp ntGhgnq dbpntug L Gpm 2ntppp

qmmqnq bp4n~ tlt~mpnGGtpbg: Pnpb mtuntpjntGp Wpurnb@ t dbmjG ppmbGmGdmG (dLi4 t~t\mpnG ntGtgnq) mmdlitipb hmdwp L m ~ t G wpm- n t f i it htlfin~db m m d b hmfimp, pmGb np d t u g m q b ~ tltlpnpnGGtp ympnt- Gm4nq mmdGtpntd, pmgb dbpnt4-tlt4mpnG 4ntlnGjmG tlmbmqqhgn~pjnt-

Gbg, mn4m t GmL tlblpq~nG-tlti4mpnG tlntlnlijmli *nNmqqtignlpjntGp, npG t~tQmpnti-bbpn~Q anbmqqtigntpjmti gmpqb t : Qtmp t G4mmp ntGhGm~ np mdbG db tltrlpnpnG ntGb nqtbpmjbli dtlumGbljm~mG L dmqGbumtpG dndtiGmGtp, ntumb QnjntpjntG ntGbG GwL mqtbpmjfiG dndtGmGtipb m- bmqqhgmpjntGGtp: Pmgb ~lpmGbg, mdbG db tlblppnG o h q m b t uli*m- QmG dbfumGbQm4mG L dmqGbum~mG dnfitiGmGbpnq, nmmb qnjnlpjntli ntlihd GmL u ~ G - u u & G ~ b G L u@G-nulbbpmjb Lfm~mqqtgntpjntGGtp:

SmG4mgmb mmndntd db2m q b p m ~ ~ n n q t dfipn~4-tlt4upnG 4nt~nIijmli dqnrln~pjntGp, u ~ l m q t i u mmndp 4yn tG i t p OGb: qbpp pqmp4qmb dGmgmb an@mqqtgn~pjntGGtipb hw2qwndmG mGhpmdli2mntpjntGp 4w@qmb t mmn-

db ~ p d b p b g : Udtlimympq q tqpp , npG ~pml~mGwGn~d t hmdtdmmwpmp @1pp

4wpqmpbq nlGtgnq mudGbpntd, mjuytiu 4n)qmb Gnpdml 4mqG t, bpp

tlti4mpnG-tlt4mpnli 4ntlnGjmG @~mqqtigntpjmG tGtip&uG dtib t u 0 G -

n u l t b ~ w ~ b f i mfumqqbgnW~mfi tGtpqbu?lbg: h m P W ~ b 4 nlfibgnrl mmndGtpntd qhpmlynnq t qmnGntd u@G-nult&pmjpG @nNmqqtgn~pjntGp, L mdtiG db tlblpnpnGb qntdmpmjbG dndtGmp #nfumqqntd t djnlu t l b l p -

pnGGtpb qntdmp~ujbfi dndtidmGtipb htm: Ujq~~&ub l p y p Qnlqnld t j-j Ijmq:

WpbG Qmpqmpbq ntGtgnq mmndGtpn~d bpm~wGmGnrd t G mqt* pmpq

fibpmG4lml 4mulbp:

Impdml 4 m d l hmdwp fimuutLb 4nrldbg dzm4qmb t m m d b mjuytu Qn>qmb qli4~nnpwbwG fi~bLI!, nPp q t ~ m ~ h p q n t d t WJG tltillmpnGGtpbG, npGg ummg@Gmp 4MmllGbpb tf ihp&~Ghpb mwpptrpntpjntGG oqmb- Q ~ @ I G mbpljpnld t (ou1rnb4~~4mG tlhhmpnlilibp): Uju ymjdmGbG pm-

qwpmpntd u ~ l f l d b ~ P ~ u P ~ G L h m t i ~ b ~ 1 b q i @ m g q ~ b pwqmGpb

t~ti4mpGGhpp: U m d b q t 4 m ~ m Q m G d q t @ hbdpntd pGQmb t G htmLjmlqpntjpGtpp. 1. U m d b Fnlnp o~mbl lm4wfi tlt4mpnGGtpb u@Gtpp qmumqnpqntd

t G hmd q n ~ q m h b , 4wd hwhmqntqwhtn L qntdmpqntd t G ~ t i ~ m n p m q b u ,

mjubGpG' S = z S i : BmGb np tlttmpnGb u*Gp A/2 t , m y m q ~ t d m p

u O G p h~bfib W ~ F W ~ ~ b 4 ~ G q m d A , hpb t~t4mpnGGtpb pbqp qntjq t, L 4llummdpnqp abq mGsma A , tat tlb4mpGGtpp pbqp 4tGm t:

I s I =AS,, nprntq S, dbbnlpjnlfip tprqntd t map u@GwbG p ~ a -

mpqmb 64.14-ntd: I L I = hLa, nprnbq La dtbntpjntGp Ijntdntd t m w d p

ntqlibpwjbG pqmGmqbG pbd: 3.U~nndb u@GqbG L nyitbpwbG dndbGmGtipp qntdwpqntd hli

qtilpnnpmytu, mjubGpG' J = L + S : UwlpujG pn~j lmmpto t G L -b L S -b dbpL dbwjG wjG wGljJntGGhpp, npnGg qtulpntd J - G wdpnqp pbq mGqmd A t' qntjq pqnd tltQmpnGGtpb q t w m d L Wuwwdpnrlp pbq wGqwd A' 4tGm pqnq tlt4rnpnGGhpb qtiulpntd:

] J I = kl, , npmtq J, dtbntpjntGp Qntqntd t m m d b GtppbG pqmG-

rnqfiG pbq: Udpnrlp mmndb u@G-nqlibpmjbG @nluwqqtgntpjmG tGhp- @mG, uqublipli' qntdmpwjbG ut@mQmG dwqGbuml+uG dndtGmb L qntdmpqbli nyitbpmjbli dmqGbum4mG q m ~ m b mlumqqtign~pjwli

tGtp&mG' AE = -psHL = -psHL COS(SL) : hGmpmqnp mpdtpGtpfi

pbqp, npp 4ntqntd t *hwm d n t l ~ ~ ~ l b ~ ~ ~ ~ d n t p j n ~ l i , hwqwump t L L S qtlpnpGlipb dbpL hGmpmqnp pntjlmmpt@ mG11JntGGtipb p@G, ~ u b G p G ' J q t Q w p b hGwpwqnp mpdtpGtpb p@G: Ja-b hGmpmqnp mpdtplitipli pGhwb

t G (La + So)+ L (La - Sa)-b dbpL: fltptdG, hGmpwqnp mpdlitrgGlipb phqp

(dn~ lm~q~hmw4~Gntpjnt~p) 2Sa + 1 t , pmgb La = 0 qliypbg, bpp J = S , L tGbp~ml.pG @hm4p hlqgqmb )t:

2. wt-ntut- usnup u ~ t ~ s r c tiphnt oqmpQm4mG t l h ~ r n p G ntGhgnq mnndGtpbg wdtliwqwpq

uytQmpG n~Gb h t b t d b mmndp, npb bpbnt tltlpnpnGGtpb uuGtpp , hwdw&wjG qti~LnnpmQmG d q t o , 4 w p q ti6 qwuwllnpqtil bpmp qntqmhtn b u d hw4mqntqmhtn, L, hmdmymmmu~mGwpwp, m m d b uuGuqbG

pqmGmmjbG pbqp' S a = 1 4LUd So = 0: ntpbdri, m w d b nu$ibp~~bG pqwG-

m q b f i B* La w p d t ~ b q b ~ n t d G t ~ ~ b f i ~ W G m w ~ b f i ~ b q p ' Ja = La + 1, La,

4wa L~ - I , tpti sa = 1 L~ = o ~ t w b g ) L J, = L ~ , tipt S, = O: qwpq t , np mmndb tGtp&wfi 4luIuqwb t tiphnt t~t4rnpnGGbpb nl L n2 qfimqnp

pllmGmwbG pqtpbg L 11 n~ 12 nulhbpw~bfi pdwGmwjbG pqhpbg: P u g ) wwGlpg, wmndntd uUG-ntqtQuqbG Jm~mqqtgntpjmG tGhp&wG lqb- dmb t La+ L So-b wpdtplitipfig L GpmGg dbpL mG4~ntGbg, ntptidG' L Ja-b mpdtpbg: U j u u u n q , hhmtdb ~ ~ d b E = E(n1, nz, II,I2, La, Sa, J,) tGtp-

4 u ~ l u q ~ b t jnp LJqmGmm~bG ~ q h ~ b g : Umbm~fi f i n ~ ~ f i m ~ d b t p h n ~ tlt~mpGfitpb d~wAudwGm4JLu wqndwG CnbdGwllmG @dmWg hwlih~n~) hmqw~mlpGn~pjntGp 9 ~ 9 ~ 1 1 ~ 6 W w W m W n t ~ ~ m f i zwm @npp (10-8i10-9 4) filitiln~ qwmdmnn4 ~mIlIwqmGg +npp t: ntpbdG, qpqndmG L ~ w n q u ~ p d ~ d q t w n t f i wmndb tltl4mPnGGh~bg fith! ( ~ W P ~ P ~ t ' npp)

qmliqntd t hbdGmljmG @hmQntd, wjubGpG' nl = I , 1, = 0, L, = ll + l2 = It L E = E(n2, La, So, Ja): b ~ q d t G p h t b t d b m m d b hGm-

pwqnp @GmllGtpb wuntuw4: 3wqnllmb mmndb b ~ p l p n ~ tltljmpnfip G ~ I J G - qbu 4qmG* n2 = 1, l2 = 0, La = 0 @hwQntd: UnmpbG qpqnqmb ~ @ h m 4 G t p ~

n2 = n = 2 ~ 6 m ~ G t p G hG, npnGg pbqp hmqmump 1; qtgb: bpnp, t p t n = 2, m q w La-G l.ppnrl t pl iwGtl 0 (S @hwW L 1 ( P #hmll) wpdtpGtpp

(hb2tglib(ip, np Lo = 12 pWGmm~bG pbdp 4~1"ul t ~ G w ~ G ~ L 0-bg n - 1 F ~ L ~ P mpdhplihpp): bpp Sa = 0 (uQGtpp hm4mqn~qwhtin hG), Ja = La GntjGyhu Qwpnrl t p G p t G t ~ tp4m mpdtp' Ja = 0, 1: Ujq tpbnt @hm~Ghpp G2wCm4-

qntd hG 2So L 2P1 ~ p h ~ m G b 2 G h p n ~ : Ujumhq mnmpbG pbdp' 2-p, qfimqnp pqwGmwjbG p a wpdtpG t , La= 0 @6mQp G~mGm4qntd t S mwnnq L

4n)qntd t S fi6m4: La= 1 @hmQp G~wGm4ntd t G P-nq, La= 2-p' D-nq,

La= 3-p' F-n4 L WIG L wGqwGntd t G h m d ~ q ~ m m u ~ m G w p m p P, D, F @dmllGtp: Ujuqtiu, n = 2 L La = 0 4I6m4p G2mGmQqn1d t 2S-nq, n = 2,

La = 1 Ubw4p'2P-nq L n = 4, La = 2 fihw4p' 4D-nq: h~nphpqwGb2b GtppLb

u p mG11JmGntd qpqntd t J-b mpdtpp, opbGmQ' 2So -nq G2qntd t n = 2, La = 0,

Ja = 0 ~WGmmjbG @hmQp, 2P1-n$ n = 2, La = 1, Ja = 1 @hm4p: LnyG

n = 2 qtqpntd, hpp Sa = 1 ( u u G t p p qntqwhhn tG), mqm La = 0 qtulpntd Ja = La + So = 1 @ h m u lunphpqwGb2p 4oGb 2SI-p, bu4 La = 1 q t w n t d

Jo-6 4wIW t pfivtGtil J a = 2 , 1 , 0 wpcttpGtip~: Ujq @ 6 ~ m w p h ~ ~ 1 -

GbzGtpG t G ' 2P2, 2P1, 2Po : qb6w4Gtpb G~wGLuQntdGbpp npn2 qhyptpntd b4Gqntd tG: OpbGwb,

2Pl (n = 2, La = 1, Ja = 1) G2wGmtptdp qtpwptpqntd t m m d p lipQnt mwp-

Pbll 4I6~4Ghpb: W p b G Qhm4, npntd tpljnt tlt4mpnGGtipb uulfiGtpp hm-

4mqn'qmhtn tfi' Sa = 0, L tpkpnlq Q1iim4, n p d u@Gtrpp qntquthtn tli'

' a = L S - F n ~ t b p w j b l i dndtGmp htm 4wqdmt~ wGljJntGp 120" t , L Ja = 1:

= ' 7 La = 1 qhqpntd Ja-G 4mpnrl t pGqntGbl t p t p wpdtp: J L S ~ti4mnp-

Giipb Qmqdmb mGtp~GGtpG t G ' 0°, npb q b q n z d J, = 2, 120°, npb qhqpntd

J, = 1 L 1 SO0, J, = 0: UjubGpC' Sa = 1 @6mQGhpp mpbyltm ( tnmm) bG,

Pub so = 0 @6m4Gbpp' ubGqltm (dbqGmQ): Ujq @6mQGtpp mmpphphln~

hmdmp bnphpqmGb2b mmnb qtpbG & L U ~ mGhn~Gntd qpqntd t (2Sa f 1)-b

mpdtpp, npp S, = 1 qbypntd 3 t , bu4 Sa = 0 qtypntd' 1 : f GqhwGn~p qby-

UqJntumQp Gtntd t , pli ~ G > L @ I ~ tGtpc$mQmG ~ 6 m 4 G t p bG hGwpmqnp hh@n~db wmndntd L bliyql~ub h ~ u p n p q m ~ ~ ~ n t p j m d p hG mjq t&6mI$i!ipp qmuwqnpqmb: t;lGhlnq qpwGbg, lpuqfitGp tGtpc&m~mG @bmbGtpb q$m- qpmd (G4.15), npntd mpqmb liG @Cim~Gbpb tGhpq$mGhpl~ dnmmqnp mp- dtpGhpp: <bhmQGtipf~ tGtpc$mGhpb 62qpbm wpdbpGtpp lppn2tfip anpd- Gm~mGnpbG, h~Ghlnq ht@tdb m m d b uytQmpbg:

< h w ~ d b mmndb uyiibmpb $mpdmpwpm\mG n~untdGmu~pn~pjntG~g h~ujmlimphpqhl t bp4n~ mnmGdGwhmm~n1pjn~G: UnmpbG. uq t4mpn~d mm- qntd t iG dbmjG w~G@ub uqb4mpu1~~G qbtp, npGp hmdmymmmulumGn~d t G 4wd fib upGqtim @ h m u g dp wjl ubGqlhm a 6 m Q mGgdmGp, 4md fib

mpbulltm @6UJWg db WL mpbqltm @ h ~ 4 UJGgdmfip, i4m ni db uyh~mpujb f i q$b, npp hmdmqwmmu~mGn~d t mpbqllim @6m&g ubGqliim *6w4 4md hmlpunm~ wGgdmGp: UytQmpG nlGb qG@ub mtup, l.ppbhu mmndGtipp db dwup mmfiu t ubGqliim, huh djnlu dmup' mpbqltm

L4.15. ' l t jhn~db tGtpql1w4wG dur4wp~w4Gtpb ~ b w q p w d

qbtp: tnyGbuQ Qmpbbp 4wp, np pGnlpjtllC1 dhp q n j n ~ p j n ~ i ntGb tp4nl mhum- lil~ hbwtd ' ympmht@ntd (dpqCm4 qbhp) L oppnh twtd ( t n m u qbtp):

bplpnpq. u y t i l p p n ~ d p m g w ~ ~ u ~ n t f i t G LUJG uulh4mpm~bfi qbtpll, n p n f i ~

h ~ d ~ ~ m m m u b m G n t d hti npLt qpqnqmb @timug 13s1 @dm4 mGgdmlip:

UQG-nqhbpmjbG @ b m q q t g n ~ p j w tGhpqbmG 4mluqwb t mwppb

~ ~ P ~ ~ B @ I (aLs - z4 ), n u m b h t w t d b (2 = 2) m m d b uyb4mpn~fi

m ~ b ~ l b m b qbtpb mfiph tp4mpn~pjn~GGtp mmpptpn~pjntGp 2mm @BP t, L Unqn~u4mG uulbQmpmjbG umpphpp h n j w u mnmGdbG qbtipp ihG pnuntd:

fG#mGntp qbtpnq h t w l d b mmndb uqtQmphG GdmG uythmp n1GtG 'pkn1 oL4mb4m4mG tlh4mpnG n~Ghgnq pnlnp mmpphpp' h n q m l Q m W l l ~ dtumrlf ib~~, gbGllp L Qmqdbtdp, n ~ u m b qpbph GnyG ~ p b f i ~ > m @ n l ~ ~ n I f i -

Glipp, hbdGmlpGntd' uTpGqltmwjb6 L mpbqltmmjbG ~mnntgqmQp, rlfim- qntd t G GmL wq mmdGbpb uyb4mpGbpn~d:

Uju m2~mmmGpntd ntunudGwubpqntd t l p q d @ t d j ~ uqhQmp~: 4mq-

d b t d b QUl~q~lpbqQ' z=48, nlumb u U & 6 - n q k i b p ~ ~ b @nFLUq~bgIllp~LU6 tGtp&mG I/mqdbtdb mmndntd db pmGb hmpjntp mGqmd dbb t , pmfi ht@tdb w w d n t d :

U~~UUIVIUIG~~ t i q w m u ~ Q ~ Uju m~brnmmGpb GqmmmQG t .

1. npn2bl4mqdbtdl1 uqtilpnpf~ m b u m G b ~ dmuntd rlfimqnq uyb4mpmjbG

9 b b ~ b mlb~f i ~ P ~ W ~ ~ F J ~ L G G ~ P P L, oqmqtlnq tGhp&mhmG @6mbfib~b @WPmdbg7 @ P ~ G ~ L WJq Q ~ ~ P Q :

2. hfihlnq q L W q n ~ u t~bu? lb mnwYbG bptp q b b b mlhpb ~ P ~ W W ~ P J ~ ~ G - Gtpbg' n p n z t ~ uud-nqtZ~pmjbG mbmqqtgntpjmG t[itpQwG 4mq- db ld f i mmndn~d:

3. <mdtidmmtl ~mqd@tfib m m d b qfimqnp utpbmjb mnmpfiG mpbq-

~bUlb u@(i-nqbbpLUjfi ~ b w q q t g n t p j w l i tfitpqfilufi filuUlpb1db w m d b q&mqnp utpbrnjfi mnmpb[i b4Gm@ u@G-n~qbbpmjbfi @n-

~mqqtgn tp jmd t l i t p a w b htm:

4. <mdnqqtl, np mjq tGtp@mG hmdhdmmwQmG t z4-bG:

u s n t ~ n ~ u ~ u ~ ~ r ~ ) t r 1. f iGp$~ub~ @i-umqqtgntpjntGGtp hG q n p b t d dbmg mqbl oymbQmlpuG

tlb4mpnGlibp n t G t g q w m d G t p ~ d : 2. nap QmyG t 4n24ntd Gnpdml4mul:

3. Ihjmphbl ~ti4~nnpmhmG dnqhlb tpbp hbdGmllmQ rlpnqptitpp: 4. QmGiia hGmpmqnp tGpwdrn4mpqm4 t mnmpwlintd u ~ G - n u l t ~ m j b t i

~ b m q q t g n t p j m htmLuGpnq: 5. bGpP t Gymmm~mhwpdu~p uybQmpwjbG qbtpfi mpbyltmmjbG

4umntgqw&pG n~untdGmubptl l p ~ q d b ~ d b L n> pti h b m t d b m w d b uybQmptd :

~ t t u u ~ t - t r tdnt3m ntuntnuut-rntuc StUULIUlJ UUU

UpmmpbG dmqGbum4mG 4 ~ 2 m b mqqbgntpjntip ~ntjup *UI hhmm- ~ ~ p p p b ~ t qtnLu u.%mpmqtjbfi: 1896p. q.2btdmGp @np&nq hmjmQmptphg dwqGbum~mG q m z w t d m h ~ r ~ q m b ~ n y u b mqpjntpb b ~ m q m j p d m l i

uqtQmpu~~bG qbbpb bhEdmG hpLn~jpp (2ttdmGp t p h y p ) : tQ.16-ntd qwmQhpqmb t 2htdmGb m p & b ubtdmG: IqliQ~npmdmq-

Gbub pLtnGtpb db@ umtqbqrnb ~ r n ~ w 4 m f i m ~ m @ hmdmutn dmqGllumlguG

ry.uzmtd m ~ m r ~ d w b C I ~ I J U ~ mqpjntpb mnmprnb bmnmqqpntdli

nqqtln~d t S u u l h b m p ~ ~ b d umpphpb *m, npnGp qpmligntd t G Gpm

uytllmpp: UiuqGbuwQmG qmzmh nqqntpjmdp mmpmbflnq Lntjup uybllmpb qtpmbhlnt hmdwp dwqfibub pLtnGbpp qwzmb nqqntpjudp zmqm@qmb hG:

L4.16. E l t t d ~ l i t ~ $flpd/l ututdurG (C' L ~ L J U ~ UrlFJnLp, S' ~ ~ t 4 ~ p u r i b G uwpp, W t~t41npludurqG~ub +lupn~jpGtip)

Onpbhpb mpqntliprnd dwqfibumljrnli quapnnld gbw~fi~4 uulb4m~u~~bG bhpb IZlir@dmG hmdmp ummg~trl hG htmLjml opbGrn~m@~pjntG6hpp.

1. U ~ q G b u m ~ m G qm2mbG nqqmhuqmg nqqntpjrndl? m w p ~ W n r l ~ ~ n ~ -

9u?l~fimfi uqhIpnpnrd j m p m p m t i ~ n ~ p uyhhmpmjbfi C$b ( Y ) b b q n t f i t '5 - A VL, V, L V, + A vL hwhmluntp~ntGGbpn~ LI qhj f inpbf i pLhnmgmb

t p t p pmqmqpbyGhpb, pGq npntd h m b m ~ t p j m f i AVL @nLbbnt~~ntGI!

hmdbdmmm~uLi t dmqCi~um~m6 qwzmfi lmp~mbn~pjm6p' A - H (G4.17, m):

2. UiuqGbumQmG qm2mb n~qqntpjmdp mmpuwnq hmnuqmjpdw6

uqh4mpntd j n ~ p m p m G ~ n ~ p a b ( v,) btqpqntd t v - A V L L v, + A V L

pmrlWPh>Ghpb, hub u b t l q ~ b ' % h ~ f i ~ u ~ ~ ~ ~ ~ d ~ , pmqWPh>l! P K W - Q ~ n t d t (G4. 17, p):

L4.17. U~wjGw4 uqt4mpwj~G q&p d t r l p n ~ d ~ dwqG~uu4wG q w ~ l n n ~ d (2bbdurG~ 6npdu.1~ bpLnyp). w) ~nyub mwplu&dwG n ~ ~ y n ~ p j n ~ G G n~rlnwhw- jug t H-bG, p ) ~ n ~ j u b murpur6d~uG n~yr ln~pjn~Gp hurd@G4Gn~d t ujG n ~ ~ r l h htm, npnq n ~ ~ r l t l l u b t H-p: 8 n ~ j g bG tnp$~~b GwL p w ~ w ~ p t ~ l G t p t ~ pbtnwgn~dGtpp:

UiuqGbumhmG qm2mntd dbwj l iw~ u q h ~ m p m ~ b G qbbpb 6 ' Q n t d p

hmjmlib t n p q t u 2 h t d ~ 1 6 ~ Gnpdull4md qmpq h p h ~ j p :

UiuqGbuwllwG qmpnntd @4Gw4 uqbQmpwJb6 qbbpp b b ~ d w 6 hmdmp ummg~@l bG q l o p ~ G u " ~ ~ u ~ n t p j n t 6 6 t i p ~

1. Ih.11~1 dmqGbumlpuG q m ~ m t d , bpp A VL << 6 v (6v-6 LpllGmU bp4nt

qbbpb dbpL pGmhm6 d Q n t d 6 t), b h G m U qbbpbg dbhp 6tqpIntd t 4, bu4 djntup' 6 pmqwqp~26bp~, p6q npntd d@dmG >map'

A v = + A v L - a/b , npwliq a-6 L b-G nt dlib, mdpnqp pqtp ha:

2. n tdtq d ~ l q G b ~ ~ 1 1 1 ~ 6 ~ ~ m n ~ d , bpp A V L > 6 ~ , QpU14Gm~ t i p ~ n ~ q&pb

@nNwpbG *mqntd t L P ~ P (Fmr lm~P>) (64.18, p): UqtQmpmjbG qbhpb CitrpdmG wju q b w p hu?lmGb t npqhu ~ m z b G - P m ~ t p h t j p :

cDnpbc gntjg t mm@u, np bpbp L mqt* qbhpbg pmqbwgwb dnt~mbq-

~hmlibpb hmdmp dmqGbum4mG qm2mntd qjmqnq uqb4mpwjbF qbbph 6tiwdluG ymrn~bplibpp Zwm mqb@ pmpq mhup ntGbG, mump q u

m~lummmGpntd 2tiG pGGmp41@1d:

pwqwqpb>p' FLx = 0, pmGb np [vim = 0: Ujmu pwqwqpb>G pGmpbGp yz hwppntpjwG dtp, npmtiq t~tilp.npnGb *UI w q p q LnpbGgb n t w

FLL = ev,H/c, pmG) np VM : yz hmppntpjmG dhp qbwjbG

mmmmGntdGbpp Gtpb~mgGhGp npytiu tiphn~' h w h m p nqqmpjn~GGbp4 qmmmIpG 2wpdntdGtpb qntdwp:

'bw2mb p w g m ~ m j n t p j m qliqpntd q q qumymlihpb hmdmp 2mpchlmG hwqwulupntdp lpqitifi t GbpljwjwgGh~

2 m w 0 r = f r (2)

mtupnq, npmiq r-p yz hmppntpjwG dtp 2ppwGb 2mnmmG t, f-p'

p ~ w ~ w n w & q m ~ m G n 1 p j m l i q n p h w g p , m-p' t~ t ihm~pGb qulGqq~bp, 00-6'

~pptuGu?)bG hu6m@ntpjn~Gp'

2 2 e mw r = f r f FLL 4md mo r = fr+-wrH c (4)

mpmmhm~mmp~ntfip: UqtQmpmjl-di qbb hm6m@nlpj~fi A ~ L @*MI- ~ ~ m f i p Qn)dntd t ~nptiGgjmG ~ t q n t d : (7) puGm&Lb9 h t m h t d t 7 np

~ ~ t ~ m p q f i ~ qbb ~nptGgjmG ~ t q n t d p t l m ~ q w b rt vo uhq~Gm4wG hw6m-

h ' ~ j m G b g L n m hmdlidwmm4wG t dmqGbum4wfi W2mb lwpqm- ~ ~ B J u G ~ , bG)p 2mm dtib 6 2 m t ~ ~ m d p hmummmdntd t Wpfind:

LnptGgb mtuntpjnulip pmgmmpnud t GmL vo h u b w ~ u p j m d p uqtQm-

pmjbG qbb ~mgm~mjnupjnttip qw2mb nulrln~pjmdp mwpwqnq bmnm-

q~u~pdmG dtp: b p p , dmqGbumlpuG qm2mb mnQtuJn~pjmdp vo hmdm- mupjmdp lp.nmmmGqtG d b q G WJG mmmmGm~Gtpp, npGg mmmmGdmG

ntqqn~pjnuGp qmqmhtn t qw2mbG, L FL=O: Um~mjG mmmmGm~p

mmmmGdmG nqqnupjmdp bmnwqqplil >b 4 w p q (t~tQrnpwdwqG~um~mG

mmpp lqGmlpG t), L x nulqnupjmdp mmpmbqnq bmnmqmjpn~dp vo

hmhm@mpjnuG qwpnlGmljtl fi L p p q : vo h w d w m u ~ m d p mwmmGqnq

mmmmGmQG mnmqblmqn~jG bGmtGubqn~pjnuG 6mnwqqpntd t xy hmppnupjmG dtp gmG4mgmb nqqntpjmdp: Ujq ymmiiumnq tl qm2mbG

ntqqmhu~mg gmG4mgmb (opbGm4' y) nI,qr(ntpjludp mmpmh@q lntjup

Lpqmpn~Gmu vo hmdwlun~pjmdp uqti4mpmjbd qbb:

LnptGgb mtuntpjnuGp ~UIgWmpnId t GmL uqt4mpu1~bG qbtipb

wnmG&bG pmqmqpb>Gtpb ~Ltnmgnudp: bpnp, pmGb np y nqqnlpjmdp

mmpmwnq 6 w n m q ~ p d m G vo hmdm@nlpjwdp pmqmqpb>p dmnmqmjpqntd

t x nqqn t~~lmdp mmmmGqnq mmmmGmw 4qdbg, u q m Gpm tllilpnpwQwG

qli4wpp lpnmmmG@ xy huppnupjwG dhp, L mmpp h@Gb hwpp pLbnmgmb:

LQ.17, m-ntd wjq ~Ltnwgntdp ywm4hp~u1b t y tqqmb uqt~mpmjbl i qbb

~ P U ~ ~ 4 m b t p t p pwpmll qbbl lGb~4, bQ>p G2mGm4ntd t , np u?lu pmqwqpbyntd ~nuuqpG wopb tlt~mpm4mG qtlpnnpG nqqqmb t H-pG qn~qmhtn ( w u y t u \n>qwb n-puqmqpp>):

&mGb np GnyG y nqqntpjmdp m m p m ~ n q ~ n ~ j u b vo 4 A K L vo - Act hmbw@ntpjn~GGtpnq p m q q p > G t i p ~ d u m m q ~ p q n t d l i G z nulqn~pjwdp

mwmmG4nq mmmwGm~Ghp~ Qnqdbg, m q w GpmGg tlblp.npmtpuG

qli4mnpGtpp ~mmmmGqtiG yz hmppntpjmG iltp, L wjq m@pGtpp GnyGqtu

4oGtG hwpp phlinmgwb, umQwjG qtpppGGtp~u pLtnmgdmG hwppn~pjntGG

n q q m h q m g t vo hmbmlunlpjmdp pmqmqppa pLhmgdmG hmppn~pjwGp:

L4.17, m-ntd wjq pLhmgn~dGtpp qwmlltpqmb liG ~l iqqmb u y t ~ m p q b G

9bhpbg 4kp q m m 4 t ~ 4 m b Wmb4 Z P P U J G ~ ~ ~ ~ P ~ , bG>p G2mGmllnud t, np ~ n t u q b G mmpb tlt4mpmlpG qm2mG nqqqmb t H-PG nqqmhmjmg

( u ~ ~ u y h u 4n>qwb o-pwqmqpb)Ghp):

x n q q n ~ p ~ w d p mWmbqnrl vo + A% L vo - A% h m b w ~ n t p j n ~ G G t p n ~

p ~ q ~ ~ b > G t ~ ~ h m n U J q ~ ~ ~ d n l d yZ h ~ ~ p n l p j ~ 6 dhp huQw~&p n q -

q n ~ p ~ n t G G t ~ d ulmmqq mUJmmfiwbGtpb Qwdbg, ntumb q t m p t uulmubt

11p w j ~ pWmQPb>Gt~b tlt4mpmbmG ~ h l l m ~ G t ~ p 4ymmqtG x mnmGgpb

zn'pp, h pm9mQPb>fihp~ bLhGt6 Up L 2ppmGuljbG p l h m g u b m@pGtp: ~ 4 . 1 7 , p-nld m~rl ~LtnwgntTGbpp qwmbtpqmb t E Qnpmqbb u l ~ ~ p ~ t p n q

(o-pLtnwgnud):

LnptGgb mbunlp~n~Gp pwgmmpld t d@w~G 2hlidmGb Gnpdml tplnypp:

9ttdmGb ~ G n f i m l t p h ~ p p L q w t G - P m M tiplntjpp hGmpmqnp t pw- gmmpbldpm~G pqmGmuJbG mtiunlp~mdp:

u ~ q p b g tGpmqptGp, np mmdG nlGb d ~ u q G nqtbpuqbG dh@mGb-

~ L L I ~ W G L dwqGbuw~mG dntltGmGtp, mjubGpG' hmz* >mnGtGp t~tQmpnGb

uLqpip: UiuqGbum4mG qmpnntd qmGqnq m m h t d tltQmpnGb nqtbbpp ~ w p q

t q p m q t ~ d b q G wjGu@ub a p p t p , npnGg qbqpntd nuqhbpmj~G findtilimb

u lpn j t~g~mG qw2mb nqqn~pjmG Ilpm pGqntGntd t mbpnqp pbq wGqmd h wpdiipGtip (mmpmbw4wG pqmGmwgntd):

fltqtibpwjbG dntltGmp h q y m b IIIqqntpj~mG dbpL 4~uqdqmb 6 mGbmG

hwdmp nrGbGp' cost? = m/l , npmliq 1-6 nuqtbpmj1lG pqmGmmjbG pbqG t ,

m-p 4nyqntd t ~ u I ~ G ~ u ~ Q w G pqmGmwjbG pbq L Q m p q t pGqnuGtl 21+ 1

hum wm4mG L pmgwumljmG wdpnqp mpdtpGtp' I, 1 - 1, . . ., +1, 0, -1,

..., -1:

<mdmPlqG dwqG~umlpuG gf lmGm~pG p@ pn4dmG hwGnGb, pntj-

p.umph@ bG dbmjG mjG mGgntdGbpp, npnGg hmdmp A m = + l Qmd 0, hbmlwpmp' (9) pmGmdLbg ~ u m m Gw Gp'

Ummgqwb mpqnlGpp hmdpGbGn~d t LnptiGgb mtiunlpjnllibg ummgqwb

(6) mpqntGpb hlim: Ujuwunq , hpti tlbQmpnGb u@Gp h w ~ # 1hGp mnGntd,

w y m p~mGmmjbG mhunlpjnlGp GnljLiybu lplm k p ~ g ~ m p b ~ dhmjG

9titdmGb Gnpbml hpbt jpp: Uju hmdpGQGmdp ymmmhm4mG tt: bpnp, hpb

dmqGbumQmG q u p p pmgwlpqntd t, m q m u y h ~ r n p ~ u j ~ G qbbpp dlujGm4

hG UJG q h q p n ~ d , hpp m w d G ntGb qntjq pqnq oymbQw4mG t~ii~mpnGGtp,

npGg qntdmp u@Gp hm#.uump t qpnjp:

"pmtq u2 = -p2 H = -p2 H ~ 0 ~ 0 , ~ L AE, = -pl H = -pl H cos B,, mpmm-