ST¨UCKELBERG PARTICLE IN EXTERNAL MAGNETIC FIELD. NONRELATIVISTIC APPROXIMATION. EXACT SOLUTIONS Текст научной статьи по специальности «Экономика и бизнес»



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ßs№ Те!

S = 1

Аниця

УРшвиеййЕПбюэди1

жптм s = i7s =

КуЩ^ . КюМЕЖЛЕВ

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^'•ппг-сши:!

икнем

riïal^N^Itir

oq

ОД

oq

cq о" о" о" о" о" о" о" о"

КЗ

'SÄ

I

ОД &

cq

I

s

0 &

1

0 &

1

н 1СЧ

+

an

"iritiävai-

h =^(Lo + So), ho = iT^(Lo - So),

hi = l(Li + Si), Ei = il(Li - Si), (<$

itotáatói

l, 2,3.

ivwiicw:

l (Br2 +2m - 2)1

— ieho — ikh2 H--f=h1--p=-hi —

VÎ 1 2\fïr

l ,, (Br2 +2m + 2)u

- /2 h3--VÎT-h3 = -¡h,

- - ikE2 + f E[ - (Br2 + 2m - 2 Ei-

y/2 1 2Vïr

l E (Br2 +2m + 2) E = ;

- /2E3--2f/Tr-E3 = ¡ho;

- f h' - m + Bf/2 h +' B2+ y/ï Vïr y/ï

+

(Br2 + 2m) 2 У2г

B2 — ikB3 + ieEi = ¡hi,

l (Br2 + 2m) + /дho H--2ff2rr-ho - iehi = ¡Ei;

.77 • rp l W (Br2 +2m + 2)

ikh + ieE2--—Bi - --—--B1 —

Д 2уЦг

— 1 +(Br> + -2m — 2 =

Д 3 2V2r

—ikho — ieh2 = ¡E2;

1 h' — m + Br'¡2 h + 1

(Br2 + 2m) 2fb-

B2 + ikBi + ieE3 = ¡h3,

l ,, , Br2 + 2m .

--1=ho H--—-ho — ieh3 = ßb3;

V2 2V2r

l Br2 + 2m --i=h2 H--—-h2 + ikh3 = ¡Bi,

Д 2 2V2r

—ikhi--T^hf2--+-h2 = ¡B3,

l f/2

2УДг

l Br2 + 2m - 2

+ f=h'i--F-hi +

V2 1 2V2r

l Br2 +2m + 2

H--ï=h3 H--—-h3 = ¡B2.

Д 3 2уЦг

omralSBi, B2, B3 vilhlhBhfjlp

Br2 + 2m - 2 Br2 + 2m + 2

—ieho--F=-hi— ikh2--1=-h3 +

2уЦг 2уДг

l dhi l dh3

+ //2 - / ~dr = -¡h

- ieh - ikE2 +

l dEi Br2 + 2m - 2

V2 dr 2yßr

l dE3 Br2 + 2m + 2

Ei

2\f2r

E3 = ¡ho;

V2 dr

(Br2 + 2m)¡

ie¡Ei--p=-h+

2уЦг

—B2r4 + (-8k2 - 4Bm)r2 - 4(m - l)2

+-8T2-hi+

(Br2 + 2m)ik

+ --r- h2 +

B2r4 + 4B(m + l)r2 + 4m2 - 4

8T2

¡ dh l dhi ik dh2

y/2 dr 2r dr y/2 dr Br2 + 2m + l dh3 l d2h1 l d2h3

+

h3 —

+

2r

dr

+ 7Г

+ ТГ-

2 dr2 2 dr2

¡2hi,

(B'r2 + 2m)¡ ¡ dho 2v

2^ ho - ie¡hi + -2 ir = ¡Ei;

ie¡E2 + ik¡h —

(Br2 + 2m - 2)ik

2yÜr

hi

(Br2 + 2m)2

4r2

h2 -

(Br2 +2m + 2)ik 2-Дг

h3+

ik dhi l dh2 ik dh3 d2h2

+ -/2 dr + r dr

+

л/2 dr dr2

¡2h2,

+

hi +

+

—ik¡ho — ie¡h2 = ¡2E2; ie¡E3 - (Br2 +/2m)¡h+

2V2r

B2r4 + 4B(m - l)r2 +4m2 - 4

sr2

(Br2 + 2m)ik

+ ^-r- h2+

-B2r4 + (—8k2 - 4Bm)r2 - 4(m + l)2

sr2

¡ dh Br2 + 2m — l dh1 + /-----1

y/2 dr 2r dr

h3+

ik dh2 l dh3 l d2hi l d2h3j

+ 7;-

+ 7;-

уД dr 2r dr 2 dr2 2 dr2

¡2h-3,

(Br2 + 2m)M M dho 2

2/2r ho - ЩЛз - T2 = M Ез

pu

+

Br2 + 2m - 2 e(Lo - So)--2/2TT-( + Si)-

Br2 + 2m + 2

-гk(L2 + S2)--/-L + Sз)+

2 2r

1 d(Li + Si) 1 dL + Sз)

+ kdL+S) + 1 d(L2 + S2)

■/2, dr r dr

гk d(Lз + Sз) d2(L2 + S2) 2¡ г i с \ +--—- = M (L2 + S2 ),

V2 dr

dr2

-гkM(Lo - So) - 6m(L2 + S2) = m2(L2 - S2);

V2 dr

V2 dr

-e(Lo + So) - г^2 - S2) + Br2 + 2m - 2

2\[2r Br2 + 2m + 2 2/2r

(Li - Si) -

-M(Lo + So),

d(Li - Si) /2 dr

1 dL - Sз )

pirIV

-eм(Lз - >3з) -

(Br2 + 2m) m

+

2y/2r

B2r4 + 4B(m - 1)r2 +4m2 - 4

st2

(Lo + So)+ (Li + Si)+

V2 dr L - Sз) = m(Lo - So);

(aril

(Br2 + 2m)гk + 2/2r (L2 +S2)+

-B 2r4 + (-8k2 - 4Bm)r2 - 4(m +1)2,T +-^-

-€M(Li - Si) -

(Br2 + 2m) m

(Lo + So)+

+

(Li+SI)+

2V2r

-B2r4 + (-Sk2 - 4Bm)r2 - 4(m - 1)2

STT2

(Br2 + 2m^k + 2/2r (L2 +S2)+

B2r4 +4B(m +1)r2 + 4m2 - 4 +--~-(^з + Sз)-

+

M d(Lo + So) Br2 +2m - 1 d(Li + S{)

/2 dr

2r

dr

гk d(L2 + S2) + dL + Sз) +

V2 dr

2r dr

+ 7:

1 d2(Li + Si) 1 d2L + Sз)

8r2

M d(Lo + So) 1 d(Li + Si)

V2

dr

+

2r dr

+

2 dr2

(Br2 + 2m) m

+ 7:

2 dr2

M2L + Sз),

2л/2т

(Lo - So) - €m(L:í + Sз)-

kd(M±SÄ Br2 + 2m + 1 dL + Sз)

У2 dr 2r dr

1 d2(Li + Si) I 1 d2L + Sз) 2(L + S )

= M (Li + Si),

M d(Lo - So)

M2L - Sз).

+ 2

dr2

+ 2

dr2

(Br2 + 2m) m

2/2r

(Lo - So) - €m(Li + Si)+

+

M d(Lo - So) /2 dr

M2(Li - Si);

pail

- 6m(L2 - S2) + гkм(Lo + So)-(Br2 + 2m - 2^k

2V2r (Br2 + 2m)2 4r2

(Li + Si)-

(L2 + S2)-

(Br2 + 2m + 2^k 2/2r

L + Sз)+

V2 dr

pal

Br2 + 2m - 2 Br2 + 2m + 2

-=-Li + 2гkL2 +--=-Lз -

2r 2r

-/2 ^ + /2 dL + 2eSo = 2mSo,

dr dr

2 + -Br2 - 2m + 2 S

2e-Lo +--^-Si-

2r

Br2 + 2m + 2 S +

- 2гkS2--^-Sз+

2r

/— dSi /— dSз ^

+ V2—i -V2-ri = -2mlo

dr

dr

82 WWjWEjTViSKIClk^Ii^^^W Ш

|a1I

lall

(Br2 + 2m)¡

2ЛЦт

dLo dSo dr dr

(Br2 + 2m)¡

(Lo - So) - e¡(Li + Si)+

- e¡ ( L 2 - S2 ) + ik¡ ( L o - So ) -(Br2 + 2m - 2)ik

¡ dLo dSo

+72 {ir - ir' - e¡(Ll - Sl)—

2V2r

(Br2 + 2m)2 4r2

-(Li + Si)-

(L2 + S2)-

(Lo + So )+

(Br2 + 2m + 2)ik

+

2V2r

—B2r4 + (-8k2 - 4Bm)r2 - 4(m - l)2

sr2

(Br2 + 2m)ik L + + 2^ {L2 + S2)+

B2r4 + 4B(m + l)r2 + 4m2 - 4

(Li+Si)+

2V2r ik dLi dSi \/2 \ dr dr

(L33 + S33)+

\ + 1 ( db2 + S \

r dr dr

ik /dL3 dS3\ d2L2 d2S2 f2 V dr + dr J + ' 2 +

+

¡ dL

8r2

dSo

(L33 + S3)-

l dLi dSi dr dr

dLo dSo l dLi dSi f^ V dr dr J 2r\dr dr J

л/2 \ dr dr J dr2 dr2 —ik¡(Lo — So) — e¡(L2 + S 2) = 2¡2L2; - e¡ ( L 2 - S2 ) + ik¡ ( L o + So ) -(Br2 + 2m - 2)ik

ik ídL2 dS2\ Br2 + 2m + 1 fdL3 dS3\

+f 1 — + —)+ 2T \dr + hi)

dr

dr

+

2V2r

(Br2 + 2m)2 4r2

-(Li + Si)-

(L2 + S2)-

(Br2 + 2m + 2)ik

+ 77

1 / d2 L1 d2SA 1 f d2L3 d2S3\

yd2 + d2) + 2 V+ ~dr2)

2 dr2

—e¡(Li - Si) -

2¡ 2Li

(Br2 + 2m)¡

2V2r

ik dLi dSi /2 V dr dr

(L3 + S3)+

\ + 1 ( d_U + S \ r dr dr

+

2УЦт

—B2r4 + (-8k2 - 4Bm)r2 - 4(m - l)2

sr2

(Lo + So)+

(Li+Si)+

k (L dS3\ dL d2S2

у/2 у dr dr J dr2 dr2 +ik¡(Lo — So ) + e¡(L2 + S 2) = 2¡2 S2;

(Br2 + 2m)ik

+ --„ m (L2 + S2) +

pirlV

+

2УДг

B2r4 + 4B(m + l)r2 + 4m2 - 4

—e¡(L3 - S3) -

(Br2 + 2m)¡

¡ dLo dSo l dLi dSi /2 \ dr dr J 2r\dr dr J

ik ( dL2 dS2 \ Br2 +2m +1 ( (IL3 (IS3 \

/2 \ dr dr J 2r \ dr dr J

-f +

8r2

dSo dr

(L33 + S33)-

+

2ЛЦт

B2r4 + 4B(m - l)r2 +4m2 - 4

sr2

(Lo + So)+ (Li + Si)+

+

+

(Br2 + 2m)ik + L + S°)+

-B2r4 + (-sk2 - 4Bm)r2 - 4(m + l)2

sr2

+ 77

1 f dL d°SA 1 f dL d2S3\

yd2 + ИГ2) + 2 V~d2 + d2)

2 dr2 dr2

(Br2 + 2m)¡

2V2t

2 dr2 dr2

(Lo - So) + e¡(Li + Si)-

¡ dLo dSo /2 V dr dr J

Br2 + 2m - lf dLi dSi 2r dr dr

(L3+S3)+

dLi dSi dr dr

ik í dL2 dS2

/2 V dr dr (

¡ dLo dSo /2 V dr dr J

\=2¡2Si;

1 í dL3 dS33 dr dr

1 ( d2L1 d2S1

+

2 dr2 dr2

(Br2 + 2m)¡

} + ¿( } + 1 (

1 ( d2L3 + d2 S3

+

2Л/2т

2 dr2 dr2

(Lo - So) - e¡(L3 + S3)-

+

M ¡ dLo

i """ "SM = 2m2 t

~dT - IT) -2м

+ (Br\/^ (L2 + S2) +

-ем(Тз - !3з) -

+

(Br2 + 2m) м 2/2r

B2r4 + 4B(m - 1)r2 + 4m2 - 4

8T2

(Lo + So)+ (Li + Si)+

+

2y/2r

B2r4 + 4B(m + 1)r2 + 4m2 - 4

+

+(ßr2 + mk(T + S )+

+ 2/2r {L2 + S2)+ -B2r4 + (-8k2 - 4Bm)r2 - 4(m + 1)2

8r2

M Í dLo dSo /2 V dr dr

гk Í dL2 /2 V dr

\ i Л

1 i dLi dSi dr dr

(Тз + Sз)+ )

ík ( i

2

dS' dr

+

8r2

(Lз+Sз)+

Br2 +2m + 1 Í dL'i

2r dr dr

M dLo dSo ^ \ dr dr J

ík Í dL2 dS2\ if

Д V dr + dr J + 2r V (

y/2 V dr

гk Í dL2 dS2

/2 V dr dr

i (d2Li ¿s + 2 I ITT2 + ITr2

Br2 +2m - 1 ( dLi dSiЛ 2r dr dr

f + dSз\

dr dr

1 í d2Li d2SA 1 í d2Тз d2 Sз Л

+ " V+ ~dT2) HT2 + HT2)

dТз dSз dr dr

2 dr2 dr2

(M + E)ML - Sx) +

2 dr2 dr2

(Br2 + 2m)M

\ + 1J dL + d2Sз

) + 2\ dr2 +

dr2

+

2y/2r

-B2r4 + (-8k2 - 4Bm)r2 - 4(m - 1)2

STT2

(Lo + So)+ (Li+Si)+

(Br2 + 2m) m 2/2r

(Lo - So) + ем(Тз + Sз)+

+(Br[ /mk (L2 + S2)+

M f dL0 dSo\ 0 2 Г

+~dT-ir) =2м Тз■

munirмв^нм*

+

2y/2r

B2r4 + 4B(m + 1)r2 + 4m2 - 4

M = -M.

M (dLo + /2 V dr +

гk f dL2 dS2

/2 V dr dr

8r2

dSo dr

Л 1 ('

1 / dLi dSi dr dr

(Тз + Sз)+ )

\ Br2 + 2m +1 / dТз dSЛ

) + 2T \dTT + HT) +

1 / d2Ll d2Sl\ 1 / d2Тз d2 S Л

V dT+ HT2) + H ~dT2 + hT2) +

pari

Br2 + 2m - 2 Br2 + 2m + 2

-Li + 2г^2 +-^-Тз-

+

2 dr2 dr2

(Br2 + 2m)M

VÎT

VÎt

2у/2т

(Lo - So) - (M + E)M(Li + Si)+

-/2+ /2 ^ + 2(M + E)S0 = -2MS0, dr dr

2(M + E)Lo + -Br2 /?m + 2Si - 2гkS2-

y/2r

Br2 + 2m + 2+ /2S -/2S = 2MLo; y/2r dr dr -

+M (dLo - dSo\ =2M2Si.

dr dr

V2\ dr

prll

1 fdL2 dS2\ гk (dТз dSз\ (Lo - So ) + (M + E)M L + S1 )- + r + -JT) — /ï{ d- + -dT) +

parll

(Br2 + 2m)M 2/2r

y/2 ( dr dr

(Br2 + 2m)M (T + s

+—2/2T—{Lo + So)+

-B2r4 + (-8k2 - 4Bm)r2 - 4(m - 1)2

(M + E)M(L2 - S2) - гkM(Lo + So)-

(BT2 + 2m - (Li+Si)-(Bl+ml(L2+S2)-

2y/2r

2у/2т

(Br2 + 2m + 2)гk.T гk (dSA

(Тз + >%) + Til ~dT + IT) +

y/2 V dr

dr

M dLo dSo

— ( ^T1 - + (M + E)M (Li - si)+

+

8r2

(Li+Si)+

d2 L2 d2 S2

+ drï+гш (Lo- So)+

+(M + E )M (L2 + S2) = 2M 2L2, (M + E)M(L2 - S2) - гkM(Lo + So)-

(BT2 + 2m - (Li+Si)-(Bl+2ml(t,T2+s2)-

2у/2т

Ива^ 5(555,232

2лЦт

(Br2 + 2m + 2)ik.T ik (dL1 dSA

(L3+S3)+7^{ d~ + d) +

V2 \ dr

dr

fdL2 dS2\ ik fdL3 dS33\ \ dr + dr ) f^ V dr + dr J

++ $ - ikM L - So)-

-(M + E )M (L2 + S2 ) = 2M 2S2;

pirlV

(M + E)M(L3 - S3) +

(Br2 + 2m)M

+

2уЦг

B2r4 + 4B(m - l)r2 + 4m2 - 4

sr2

(Lo + So)+

(Li + Si)+

(Br2 + 2m)ik L +

{L2 + S2)+

—B2r4 + (-sk2 - 4Bm)r2 - 4(m + l)2

sr2

M ^dL0 + dSo

уДК dr

i —

dr

Br2 +2m - 1/ dLi dSi 2r dr dr

ik dL2 dS2 — К dr +

dr

1 f dL3 dS3 2r dr dr

(d2Li + d2SA V dr2 + dr2 ) + 2r V

1

2r dr2

(Br2 + 2m)M

(L3 + S3)-

dLi dSi dr dr

у

А-

'd2L3 d2 S ■

dr2 dr2

2уЦт

(Lo - So) + (M + E)M(L3 + S3)+

+M(dL - dSo\ =2M2^ dr dr

V dr

(M + E)M(L3 - S3) +

dr

(Br2 + 2m)M

+

2уЦг

B2r4 + 4B(m - l)r2 + 4m2 - 4

sr2

(Lo + So)+

(Li + Si)+

+

(Br2 + 2m)ik + l^r L + S2)+

—B2r4 + (-sk2 - 4Bm)r2 - 4(m + l)2

sr2

M ^dL0 + dS0

уДК dr

dr

)

Br2 +2m - 1 Í dL1 dS1 2r dr dr

(L3+S3)-

dLi dSi dr dr

- M ulo - цл = 2M2s3_ уДУ dr dr J 3

LítiBíegjeitsrajtar^Efls^sDvedjcin

Br2 + 2m - 2 Br2 + 2m + 2

-Li + 2ikL2 H--1=-L3-

(r

- —idL - d3) + 2So(M + E) = —2MSo,

у/2т

2ELo + -Br2 ~2m + 2 Si - 2ikS2-

уЦт

Br2 +2m + 2 ~f2r

s3 + ^f -si — sa

\ dr dr J

(Br2 + 2m)MSo + V~2MV+

2r

dSo dr

-B2r4 + (Sk2 - 4Bm)r2 - 4(m - l)2 r

+-sr2-Ll +

(Br2 + 2m)ik + 2V2r L2+ B2r4 + 4B(m + l)r2 + 4m2 - 4

+

sr2

L3+

1 dL1 ik dL2 Br2 +2m +1 dL3 + ~--^ + 1 -;— +-^--;- +

2r dr dr

2r

dr

1 d2L1 1 d2L3

+2 Id + 2~dd + 2MELi = 0, (Br2 + 2'm)M Lo + ^mL - 2(M + E)MSi +

V2r dr v '

—B2r4 + (Sk2 - 4Bm)r2 - 4(m - l)2

+-sr2-Ll +

(Br2 + 2m)ik + --. ЛТ L2 +

+

2л/2т

B2r4 + 4B(m + l)r2 + 4m2 - 4

sr2

L3+

1 dL1 ik dL2 Br2 +2m +1 dL3 + -z--^ + 1 т- +-^--;- +

2r dr y/2 dr

2r

dr

1 d2L1 1 d2L3 „ ,

+1 iL+2 -L=2M JS-

2MEL2 - 2ikMSo -

(Br2 + 2m - 2)ik

-Li + -Si )_ (Br2 + 2m)2

4r2

L2

ik dL2 dS

72 V +

dr

' dL3 dS33 dr dr

1 fd2L1 d2S1

+ 2

+

dr2 dr2

0 + f[

) + 1 (Id + d2) + —2(M + E)MS2 - 2ikMLo -

ik dLi l dL2

H---1 H---2

л/2 dr r dr

2уЦг (Br2 +2m + 2)ik 2 —r ik dL3j d2L2 у/2 dr dr2

Li

L3+

1 ( d2L3 d2S3

(Br2 +2m - 2)ik

+ (Br2 + 2m)M (Lo - 'o) - (m + E)M(L3 + S3)-2 2r

(Br2 + 2m)2

4r2

L2 -

2уЦг

(Br2 +2m + 2)ik 2 —r

Li

L3+

о

о

+ t^dL- + i dL^ _ j^dL^ + d2L2 = Im 2s у/2 dr r dr y/2 dr dr2 '

(Bl/MMso - -Ли^ + 2MLE+

2r dr

'iTi + 1 d + 2ME - k2-

dr2 r dr

--2---;--Bm\ Lo+

B2r2

+

B2r4 + 4B(m - 1)r2 + 4m2 - 4 8Г2

+ (Br2 / 2m)ik T +

Li +

+

1

2y/2\ dr

d

4 ""■') + Br2/2 - 1 ^

Li +

+

1 (d m + Br2/2+i

+

2y/2r

-B2r4 + (-8k2 - 4Bm)r2 - 4(m + 1)2 8Г2

2У2 VÎT + ' IL = °■

Тз-

Br2 +2m - 1 dL1 гk dL2

IFçicitiïuciiimai/lHîîviilÎÊnciflêîeîlIy

(h + -d + 2ME - k2-

dr2 r dr

2r

dr y/2 dr

+

m B2r2

--2---:--Bm) Lo+

1 d,3 1 d2Li 1 d2L3 n

+---3 +---1 +---3 = О

+ 2r dr +2 dr2 +2 dr2 '

4

+

1

- Vîml + (-Br2 + 2m)M

+

dr ' y/2r

B2r4 + 4B(m - 1)r2 + 4m2 - 4 8Г2

+ (Br2 / 2m)ik T +

Lo - 2(M + E)MS3+

(Nibm-ifi + N3am+if2 ) = О. (J) COnstf3, tteneq QtcteinthB

Li +

2y/2

|вайгШ Lo

Nibm-ifi + N3am+if2 = О.

lFïîe€>âciffÈîeî1iclci^crB|ïEin[l)

bm-lfl = Cif3, am+if2 = C2f3,

&

2y/2r

-B2r4 + (-8k2 - 4Bm)r2 - 4(m + 1)2

+-st-L3-

Br2 +2m - 1 dL1 гk dL2 + 1 dL3 +

for

Nibm-ifi + N3am+if2 = = (NiCi + N3C2)f3 = О ^ NiCi + N3C2 = О.

2r

dr y/2 dr 2r dr

1 d2L1 1 d2Sl 1 d2L3 „ ,

+ + т;-Г2- + X —т~2з = 2M2 S3.

tii

2 dr2 2 dr2 2 dr2

Wéaanattd rrneiMcertJcvn^ûertgeï^in

M+E АЩПЩ*

^(ЦЭД " Inrr'llmiTvifi rñttrr* _ ~

S2j S3 ' VÇ4/V!

rete

( d2 1 d l2 (m - 1)2 + i d + 2ME - k2 - (-^

d2

1 d

— + -— + 2ME - k2 -

dr2 r dr B2r2]

(m - 1)2

4

Bm

l-

О, L-

N-fi; 2

dr2 r dr

d2 1 d „, , „ l2 m — + --T + 2ME - k2 -— -

dr2 r dr r2

B2r2]

B2r2

- Bm) L- =О, L- = Nif-;

4

' d2 1 d ,, ^ , 2 m2 — + i — + 2ME - k2 - m -

dr2 r dr r2

d2

Bm

1 d

L2 = О, L2 = N2f3;

TT + -— + 2ME - k2 -

dr2 r dr

B2r2]

2 (m +1)

Bm

B2r2

L3 = О, L3 = N3f2;

- Bm) L2 = О, L2 = N2^3;

+ 1-— + 2ME - * - (m+it

dr2 r dr r2

m

4 d2

— + — + 2ME - k2 -

B2r2

1 d

dr

- Bm\Lo = О, Lo = Nof3;

B2r2

- Bm)L3 = О, L3 = N3f2;

aittteàc^araïtrart

N-C- + N3C2 = О.

^ Ивд^^ 5(555, Ш

r

4

2

r

4

4

ПЬШОД

C1 = f X - B, C2 = f X + B, _

X = 2BN = 2ME - k2. Q vithpacrctes

1 -(2a1 + 1)B + 2ME - k2 - Bm

+2-B-Fl = о

(2a1 + 1)B - 2ME + k2 + Bm ai = -2BB-, Yi = 2ai + 1.

Ф = e-iEl tN1

l

о о

о

о

-iEst^T 11

+e-iE3t N2

о

о

fi + e-iE2tN3

/о\

-iEstMo о

W

о

0

1 о

InadtrlDCftt^drdsictEB

f2 +

ai = +2jm — lj, Yi = jm — lj + 1,

f3 + e-iE3tNo

f3(r).

ai

k2 + B(jm - lj + m +1) - 2ME

2B

i = -ni

tlïtfriyroniïicoriiliora i = -ni gves

k2 B ( jm - lj + m +1А /ft

Ei - 2M = Мь + --^-). W

Îfet^^ iv®(i^iiUiti(rriïd|Diinfcrieïifel^vecft

x = Br2/2,B > о.

d2 Li l dLi -1 H---1 +

dx2 x dx

d2 L2 l dL2

2 +--т2 +

Li = xlm-1l/2F-x/2F(-ni, jm - lj + l,x)

l l 2ME - k2 - Bm

---1---

4 2 Bx

1 (m - l)2

dx2 x dx

d2L3 1 dL3

dx2 x dx

Grœtreq(Q

Li = о,

l l 2ME - k2 - Bm

—i---

4 2 Bx

(0

k2 B

El - 2M = M[ni +

n

jm - lj + m + l 2

,

l m2 4 x2

L2 = о,

W

L2 = x\m\/2F-x/2F(-n2, jmj + l,x),

n + jm±pЛA) , (4)

k2 B jmj + m + l

E2 - 2M = MV2 +-2

l l 2ME - k2 - Bm —+---

4 2 Bx

l(m + 1)

4 x2

L33 = о.

Ю

L3 = x\m+1\/2F-x/2F(-n3, jm + lj + l,x), ( jm + lj + m +l\

ь+-—^—).

k2 B ( jm + lj + m +1

E3 - 2M = M{m +

L1 = Xai eblXF1

йшясп

d2Fi ,n , ,dFi

+ (2ai + 1 + 2bix)—1 +

dx2

dx

+

— (4ь2 - —)x +7

1 4a2 - (m - 1)

2

4

+

1 saibiB + 4biB + 4ME - 2k2 - 2Bm + 4 B

Fi = о.

±-Im — 11, bi = --

Ic^nI^£^ííl(ГCfCIГiУгtl^rCf(n£llП^Ei

d2F1 dF1

x—2 + (2ai + 1 - x)lx+

4

x