!
"
"
$"
$
%#
"
%
"
"
!" $
"
"
!"
$)
%
$
!"
+ "
(
! ""
""
*
#
"
!
#
"
"
.
%#
!
"
.
!
""
! ""
"
!
*
* !"
!
!,(
,
""
"
#34
&"
!
6
#/
+" & "
!
" &"
Ψ$ % =
6
+
−
$ %
+
5
6
= 3# 7
−
$ %
5
0
Ψ=
"
−
$
5
"
"*
"
.
=
(
"
−
+
5
%0
+
−
(
0
5
!
+
(
& !
−
5
""
" &"
0
"
∂Ψ
∂
! !!
#
-0-
#
!
7
" &"
"
"
#
=
"
"#
(
!
+
&
!"
#
#
0
&
(""
"
.
&
3
"!"
"
"
,($ %#
"
!
!" #
!!
(""
,
!
" !
" !
" &
!!
"
"
" &"
!
%
"
"
(""
1Ψ $2% =
#
,
"
$
!"
!
*
!"
%
"
!
$
"
"
#-
""
'
&
"
"
"
%#
"
!
!
+
""
#
"
&"
"
!
=
**"
!
−
$ %
"
−
(
−
+
5
+
5
"
−
(
=
5
=
−
=
(
−
− $
(
#;
−
% 5
"
!
5
#9
"
0
"
1
:2
5
=
−
(
(
" "
=
0
−
"&
! ""
# (
."
0
""
− ω2
(
5
0
+
=
−
−
5
"
(
(
0
"
−
−
+
5
&"
−
!
−
$ %
0
!
+
5
#9
+
5
−
−
(
0
− ω2
(
+
(
&
−
% 5
0
−
ω2 =
&"
− $
#
.
& "
!,(
1
"&
!
$2%
#
!
,(
= 30
!,(
$2%
= 2# 9
&"
$3%
! ""
=30
"&
−
=
!!
!
− ω2
(
""
−
=
0
(
.
$ (%
− ω2 (
(#
.
2
&"
" "
&"
−
= 3+
!
(
$ ((%
((
− ω2 ((
((
2
,
$ω % #
($ 0 % = $ %
.
&
$ %=
(
&
$ω (%
− ω2 (
( :−
2
"
!
!
,
0
!
!
"
$ %=−
→
&
#
<$ω2 − ω % 5 6=
ω2 − ω
6
$% ≅
6
6
$ω2 +ω %
−3
ω2 + ω
6
"
!
− ω2 (
(#
!
+
$ω2 −ω %
−3
ω2 − ω
!
#9
.
$ω2 −ω % 5 6
$ω % #
=
""
!
6
$ %=
"
$ (%
!
(
−
(
2
"
. "
$ %
!
"
−
"
!
#
<$ω2 − ω % 5 6=
#
$ω2 − ω % 6
9
8
"
&
""
6
2
0
3
#
$ω2 − ω % 6
6
!
!"
"
!!
!"
&
.
!
!
!
.
"
&
& (
>
" &
# !
"
# / &
""
!
"
"
!
0
""
!
0
"
"
""
−
!!
"
!
!
# )
"
"
!
!
"
!
!
!
!
"
"
#
0
&
& "
"
6
"
0 &
(
!
&
""
#
#
#9
?@
"
<
!
(
!
#
"
#
0
&
!
!
<$ω2 − ω % 5 6=
$ω2 − ω % 6
"
!
$3%
!
!!
" &" #
A
A &
"" .
B
& "
$3%
0
!
ω ≠ ω2 0
"
&
!
0
!
!
"" .
>
+*
0
&"
&
! ω ≠ ω2 #
& "# 9
""
$
"&
"" &
""
ω 0 ω2
&
"
"
!!
"
1/
"
" #
$ %0
!
" & "
∆ #
"
!
?
&
!
!
#
!
&
+" & "
!
$6%#
$6%
ω
!!
#
(
!
!
""
D
" &"
#7
!!
#
0
""
!
!
&
,
,
"
!
#
"
!!
!
&
"
" "
#A
"
"
&
" $ "
" ,
%6 + φ $ % + $ %
0
"*
"*
&
"#
"
&
"*
"
"
"
"
F
!" 0
"
"
E
"
"
φ
/ "
"
"
"
3
$ −
6
ω#
&" # 7
"
,
"
!!
& "
(
=
%
!
"
#/
A
"
" & "#
!!
& "
"
!
" !
"
#
#
-
!
C
$ %
!
!"
" %#
"
(
"
!
-
!"
" 0
# 9
,
0
""
!
=
" 1
3
6
6
"
+
""
−
"
= 2 %#
6
"
"
""
& !
6
6
6
H φ#
"*
6
!
"
"
"
0 (
"
*
!!
#
&
(
*
∇# = 2 #
/ "
!
!
"
#
!
&
"
"
"
;
""
# 9
"
( "
""
%
φ
!
#
"
0 − ∇#
!
$
6
,
&
$ # + # %+
&
$D
!
1
!
!
(
! ""
$ # + # %
<
− ∇# + 6 # #
!
2
ε#
ε
$ # −ω %
0
&"
"
"
!
"
#
"
< 0
!
"
2
6
2
"
""
*
"
6
5
ε# = 2 #
&
.
%0
&
#
""
"
*
=
! ""
&
#7
!
&"
ε#
""
!!
"
"
==
!
ε
$
0
"
∇# = 2 #
$ # −ω % #
!
"
2
&
!
/ "
" :
!
"
0
# =
&"
&
&
,
=+ 6
0
"
" "
!"
!
" &"
#
G
"
&
.+
−
$
"
%
&
#
,
"
"
" "
"
"
"
"
#
(
!
#
"
"
&"
"
,
"
.
"
=
$
"
"
&"
#6
− #
&
!
= 2 #9
!
!
!
&
"
.
.
0
!"
,
!
"
!
.
!"
"
%
"
.
!"
!
"
!
" !
#
"
!
&
&
"
0 0
<
=
0 0
$
0<
&
! .
" !
0
(0"(0 ( ≠ 20
0 0
"
2:
"
""
0 ==−
0<
(0"(0 ( ≠ 2
0 0
""
!
"
" #
0 ==2
0 0
"#
−
$
( % (0"(0 ( = $
" J-
&"
0 (0"(0 (
"
0 = (0"(0 ( =
−
≠2#
""
0 0
(0"(0 ( ≠ 20
0 0
;
D
D
*
0
0 ==
= ∇×
. ""(
#9 !
"
<
!
#
&
6
&"
"&
"
(
""
−
% (0"(0 (
(%
(0"(0 ( #
0 0
" !
&"
0 & "#
!
"
!
#
,
K
"
I
< *0.=
"
(0"(0 ( ≠ 2
0 0
!
"
.
J0
0 0
<
−
(%
$
0 = (0"(0 ( =
0 0
−
$
(0"(0 ( =
0 0
" "
&
% (0"(0 ( =
−
(%
(0"(0 ( ≠ 2
0 0
"
!− # #
&
6
6
:
(
N
(
M (
(
($ (+ 3% + $ + 3% )
($ (+ 3% − $ + 3% )
($ (+ 3% − $ + 3% )
!
"
"
"
"
"
""
"
&
"
&"
! 0
$θ 0 φ %
(
"
"0"(
0< 6 0 = = 6 6 $
6
+
6
6
0 0
""
%
0< 6 0 =
(0"(0 (
:
(0"(0 (
6 ( ($ (+ 3% + $ + 3% ) = ( ($ (+ 3% − $ + 3% ) #
6
"
$ (+ + 3% 6 − 3 $ (− 3% 6 − 3 = 2
"
"
±3 # 9
(
"
(0"(0 ( #
0 0
"
$θ 0 φ %
< 6 0 = (0"(0 (
0 0
6
"
(0"(0 ( #
0 0
0
$θ 0 φ % Ω ≠ 2 # 9
6
0 0
(0"(0 ( #
(0"(0 ( =
0 0
2
!
"
(
N
= ±3
"
!
&"
(% 6
"
"
( % (0"(0 (
0 0
!!
!
$θ 0 φ % $θ 0 φ %
"
−
&
∆
. "
(0"(0 ( = −
0 0
$
!
−
$
(0"(0 ( #
0 0
$
0 0
(−
1
=3
"(:":2#
"
θ
&
& θ
."
− #
*+
""
!-#
"
" !
∆ = ±3 #
9
"
"
"
"
!!
!
"
$
#
"
!!
- !"
"
"
%
" &
"
" #
"
" #
0
" "
"
"
!
0 0
"
" !
#
(0"(0 (
. "
"
7
"
!
!
"
(
!!
!
"
"
#
"
! 0 0
!
&
!
#
L
(0"(0 ( #
"
#
!
"
;
0
&
"
! "
""
!"
0 P
#@
D
0
"
&
1
$
$0%
$ 0 %=
"
!
&
!
!& "
Q
&
"
3 ∂6
# 6 − ∆% $ 0 % = 2
6
∂
&!
0σ
$ %
$ % $ %
""
&"
"
3
"
$ %
(
$ %
(
&
"
"
*
#
!"
!
"
&"
""
!0
.
&
ω
!
"
"
"
!
&
&
$ % $ %
&
$%
:
ω
"
$% $ %
:
!
$ % =2#
6
6
!&
1∇# = 2
/ "
"
O
!
#
""
*
(""
*
""
!
. ""F ! "
-.
!"
""
!"
! ""
#
"
"
!
"
*
""
.
!
""
-"
!!
&
"
$ %#
R
=δ
0 (
* #
$0%
!
9
! $%
!"
! ,
!
@
""
# -.
"
!
#
∂
$ 0 %=−
$ % $ %
∂
= ∇× =
$ %∇ × $ %
=−
ε =
"
!"
/
&
6
+
3
6 µ2
6
%
R
.
"
A
3
$ ε2
6
""
"
!
!
"&
!
−
A
&
!
" !
! $ %# A
!
0 # #0
=2
&
&"
"
S
,
!
"
&
A
R
&
&
""
""
0
!
"
!
"
"
"" &
&
.
"
!
,
#A
"*
"*
"*
"
"
7
""
!
0
,
T =
,
! ""
"
T" =
,
δ
$%
"
(
0 (
3 6 3
T + ω
6
6
"
6
6
T
""
#9
"
+
!"
R
!
!
< T 0 T (= =
"
!
""
#9
!
"
0
"
!
,
"*
0
$ %
"
"
0
!
!
"*
&
!
&
&"
,
"
!
"
"
"
"
&
"
!" #,
!
"
!"
(
"
!
*
&
"
!"
.
!
#
E
!
"
7
!"
#
&
(
0
-
=
3
6 ω
=
!!
6
ω
)=
+
ω
+
+
+
&
,
"
"
0 (
#
" +
."
.
"
!
"
9
:2
!
*
*
!
#
#
$
"
7
"
!
9
" &"
"
0
"
$
"
"
!"
ω
T=
!"
%
!
ε2
35 6
$ T + T+ %
% N#
$
"
#
&
"
N
δ
< T 0 T (= =
&
""
*
"
"
.
"
9
&
!
3
#
6
3
#7
6
"
"
ω 6T 6 + T 6 + ω $T T − T T %
3
ω 6T 6+ T
(
6
"
(
,
+
!"
""
&
%
!"
"
"
"
#
#
0
H
0
"
0
$
!
"
" (
0
"
&
0
σT + =
$ .
σT − =
$
σT R =
"
$
%
$σT − + σT + %
!
*
"
" &"
"!
+
$
!
3
= $
6
T
3
ω2σT R # 7
6
%σT R =
−
$ω2 −ω %
σT + T U
$ω2 +ω %
ω
− $ω2 −ω %
#7
.
+3 #
"
(
V
" (
"
,
ψ$ %
(
" =− λ
&
+ 3" 0 " = − λ
"
= T
+ 3" #
V
$ %−
%
!
&
"# A
!
""
#
" ! "
(
,
ψ$ %
! ""
"&
"
$λ
$ %=
$6λ
+ 3% #
8
"
"
!
" + λ 6 $ + 3%" = 2 #
"
+ 3% 0 " $ % = −
! "
&
"
&"
"
&
.
"
" $ %=
"
"
!
"
± ω2
""
=
"
&
+" $ % ! # 7
#9
0 σT ± $ % = σT ± $2%
#
"
"
− $ω2 +ω %
+ ω
"
"
0
0 T + $ % = T + $2%
""
" *
!
= − T# T
!
$ω 2 + ω %
λ $σT + T + σT − T + % #
" (
!"
− ω
&
""
T
.
%5 #
0 σT − T U
""
"
!"
ψ $ % =" $ %
$
T$ % = T$2%
0 σT − T + U
&
35 6
#
,
!=
"
ε2
(
!
%
"
&
0 σT + T + U
.
!
λ=−
!
,
0
0
= λ $σT + + σT − %$ T + T + %
∴ T!
#
%
"
,
!
%
−
!
&
$λ
$ % =" 6 $ % =
""
+ 3% #
6
$λ
+ 3% #
! "
"
""
6# ,
&
W
""
&
W
"
""
""
"
""
&
#
*
!
""
"
!"
!"
&
"
"
.
#
#
" $ %
&
"!"
$6λ
" $ %6
&
!"
" =
&
−
6
α
6
α
E
#
+ "
&&
!
−
# $ %=
""
#
!
+ 3% #
!!
&
+
=
!
$6λ
E
" !!
"
+ 3%
W
""
""
$R%#
A
$R%
' &
"
!
+ "
#
,
"
!
# ; !"
.
.
"
"*
.
&
"
!
+3
#
0
"
"
!
!
!
&
"
.
±3
!
*
!
"
!"
"#
* !"
+ "
* !"
"
"#
( )
3#
P
6#
P
P
! ""
"
"
#
&
R#
"
@
0 ) & X#
@
0
0 /
!!
4
#4
*
>
"
&
!
© Copyright 2026 Paperzz