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- 20 -
Ihemq_ggu_\ujZ`_gby
-
iha\heyxlgZclb\ujZ`_gby^ey\_jhylgh
kl_c
P
0
b
P
i( j)
\BFI
21
ggg
−=∆
, (27)
∂
∂
+
−−+
=
−
∂
∂
⋅−=
=
=
−
−−
0
21
2
0
2
)(
)]1()1([
2
exp
)(
ˆ
2
exp
t
z
iiiii
t
TT
i
t
H
gg
MMII
H
t
THS
P
!!
α
π
. (28)
<ijhkl_cr_fkemqZ_dh]^Zkibgy^jZ
I
=
2
1
hlebq_ghlgmeylhevdhfZljbq
gucwe_f_glk
m=
2
1
−
Ijbwlhf\ujZ`_gb_kms_kl\_gghmijhsZ_lkyb\kem
qZ_ihklhygghckdhjhklbbaf_g_gbyfZ]gblgh]hihey
t
H
∂
∂
=
ijbgbfZ_l\b^
⋅+⋅
=
gg
D
P
i
)(8
exp
21
2
!
(28a)
Ihemq_ggu_\ujZ`_gby^ey\_jhylghkl_ci_j_oh^h\fh]ml[ulvbkihevah\Z
gu ^ey ZgZebaZ \_jhylghklbg_jZ\gh\_kgh]h aZk_e_gby ljbie_lgh]hkhklhygbyjZ
^bdZevghciZju\aZ\bkbfhklbhliZjZf_ljh\BFI
AZdexq_gb_
<hafh`gu _f_oZgbafuklZjlh\h]h\ha^_ckl\bykeZ[uobfimevkguofZ]gbl
guoihe_cgZdhg^_gkbjh\Zggu_kj_^uijhZgZebabjh\ZgugZdhgdj_lghfijbf_j_
djbklZeeh\
Cz-Si
\u[jZgguo \ dZq_kl\_ l_klh\h]h h[t_dlZ <iheg_ \_jhylghqlh
ih^h[gu_ f_oZgbafu fh]ml hdZaZlvky ihe_agufb ijb bgl_jij_lZpbb wnn_dlh\
\ha^_ckl\by BFI gZ ^jm]b_ihemijh\h^gbdbG_bkdexq_ghqlhjZkkfhlj_ggu_
ih^oh^udZgZebam\ha^_ckl\byBFIfh]ml[ulv\hklj_[h\Zgub^ey[he__rbjh
dh]hdeZkkZh[t_dlh\\dexqZyhj]Zgbq_kdb_fZl_jbZeub[bheh]bq_kdb_kbkl_fu
- 20 -
Ihemq_ggu_\ujZ`_gby - iha\heyxlgZclb\ujZ`_gby^ey\_jhylgh
kl_cP0bPi( j)\BFI
∆g = g1 − g 2 , (27)
ˆ T g_^bZ]
2
2π S H α 2
= exp i i i [ I ( I + 1) − M ( M − 1)]
Pi = exp−
−
⋅
i i
. (28)
! ∂ 2 ! ∂ H
(− H T T ) ( g1 + g 2 ) z
∂t
− −
t =0
∂t t = 0
<ijhkl_cr_fkemqZ_dh]^Zkibgy^jZI= 12 hlebq_ghlgmeylhevdhfZljbq
gucwe_f_glkm= − 12 Ijbwlhf\ujZ`_gb_ kms_kl\_gghmijhsZ_lkyb\kem
∂H
qZ_ihklhygghckdhjhklbbaf_g_gbyfZ]gblgh]hihey ∂t
= ijbgbfZ_l\b^
D 2
Pi = exp (28a)
8! ⋅ ( g + g ) ⋅
1 2
Ihemq_ggu_\ujZ`_gby^ey\_jhylghkl_ci_j_oh^h\fh]ml[ulvbkihevah\Z
gu ^ey ZgZebaZ \_jhylghklb g_jZ\gh\_kgh]h aZk_e_gby ljbie_lgh]h khklhygby jZ
^bdZevghciZju\aZ\bkbfhklbhliZjZf_ljh\BFI
AZdexq_gb_
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