<span class='text_page_counter'>(1)</span><div class='page_container' data-page=1>
Clear
A
T, h, m, kb, chivc, chi0, epxi,
Ω
l , qd, Lx, Ly , Lz,
dt, E0, Ef, k
Α
, k
Β
, En
Α
, En
Β
, En
Η
,
nx
Α
, ny
Α
, nx
Β
, ny
Β
, nx
Η
,
ny
Η
,
i, j, l, n,
E
Α
, E
Β
, f
Α
, f
Β
, T, ND, HS, Nq,
Ω
, q1,
q2, q3, q4, d1, d2, d3, d4 , H1, H2, H3, H4, B, P, p1, p2
E
;
T
=
200;
h
=
1.054 10
-34
;
m
=
6.097 10
-32
;
kb
=
1.38066 10
-23
;
chivc
=
10.9;
chi0
=
13.1;
epxi
=
12.5;
Ω
l
=
5.556 10
12
;
qd
=
<b>108</b>
;
Ly
=
200 10
-10
;
Lz
=
100 000 10
-10
;
dt
=
1.6 10
-19
;
E0
=
10
-5
;
Ef
=
0.5 10
-18
;
k
Α =
10
9.25
;
k
Β =
10
9.3556
;
<b>nx</b>
<b>Η =</b>
<b>1;</b>
<b>ny</b>
<b>Η =</b>
<b>1;</b>
<b>nx</b>
<b>Α</b>
<b>:</b>
<b>=</b>
<b>i;</b>
<b>ny</b>
<b>Α</b>
<b>:</b>
<b>=</b>
<b>j;</b>
<b>nx</b>
<b>Β</b>
<b>:</b>
<b>=</b>
<b>n;</b>
<b>ny</b>
<b>Β</b>
<b>:</b>
<b>=</b>
<b>l;</b>
<b>En</b>
<b>Α</b>
<b>@</b>
<b>Lx_</b>
<b>D</b>
<b>=</b>
<b>h</b>
<b>2</b>
<b><sub>Pi</sub></b>
<b>2</b>
<b>2 m</b>
<b>nx</b>
<b>Α</b>
<b>2</b>
<b>Lx</b>
<b>2</b>
<b>+</b>
<b>ny</b>
<b>Α</b>
<b>2</b>
</div>
<span class='text_page_counter'>(2)</span><div class='page_container' data-page=2>
<b>E</b>
<b>n</b>
<b>Η</b>
<b>@Lx_D</b>
<b>=</b>
<b>h</b>
<b>2</b>
<b>Pi</b>
<b>2</b>
<b>2 m</b>
<b>nx</b>
<b>Η</b>
<b>2</b>
<b>Lx</b>
<b>2</b>
<b>+</b>
<b>ny</b>
<b>Η</b>
<b>2</b>
<b>Ly</b>
<b>2</b>
<b>;</b>
<b>E</b>
<b>n</b>
<b>Β</b>
<b>@Lx_D</b>
<b>=</b>
<b>h</b>
<b>2</b>
<b><sub>Pi</sub></b>
<b>2</b>
<b>2 m</b>
<b>nx</b>
<b>Β</b>
<b>2</b>
<b>Lx</b>
<b>2</b>
<b>+</b>
<b>ny</b>
<b>Β</b>
<b>2</b>
<b>Ly</b>
<b>2</b>
<b>;</b>
E
Α
@
Lx_
D
=
h
2
<sub>k</sub>
<sub>Α</sub>
2
2 m
+
En
Α
@
Lx
D
;
E
Β
@
Lx_
D
=
h
2
<sub>k</sub>
<sub>Β</sub>
2
2 m
+
En
Β
@
Lx
D
;
f
Α
@
Lx_
D
=
1
ã
HEΑ@LxD-EfL
kb T
<sub>+</sub>
<sub>1</sub>
;
f
Β
@
Lx_
D
=
1
ã
HEΒ@LxD-EfL
kb T
+
<sub>1</sub>
;
ND
@
Lx_
D
=
f
Α
@
Lx
D
-
f
Β
@
Lx
D
;
HS
@
Lx_
D
=
12
2
<sub>dt</sub>
2
<sub>Ω</sub>
<sub>l</sub>
ND
@
Lx
D
epxi
H
Lx Ly
L
2
Lz Pi
2
1
chivc
-
1
chi0
;
Nq
=
1
ã
hΩl
kb T
-
<sub>1</sub>
;
q1
@
Lx_,
Ω
_
D
=
k
Α
2
+
2 m
h
2
H
h
Ω -
h
Ω
l
+
En
Η
@
Lx
D
-
En
Α
@
Lx
DL
;
q2
@
Lx_,
Ω
_
D
=
k
Α
2
+
2 m
h
2
H
h
Ω +
h
Ω
l
-
En
Η
@
Lx
D
+
En
Α
@
Lx
DL
;
q3
@
Lx_,
Ω
_
D
=
k
Β
2
<sub>-</sub>
2 m
h
2
H
h
Ω -
h
Ω
l
+
En
Η
@
Lx
D
-
En
Β
@
Lx
DL
;
q4
@
Lx_,
Ω
_
D
=
k
Β
2
<sub>-</sub>
2 m
h
2
H
</div>
<span class='text_page_counter'>(3)</span><div class='page_container' data-page=3>
d1
@
Lx_,
Ω
_
D
=
4 Pi2<sub>nx</sub><sub>Α</sub>2
Lx2
+
4 Pi2<sub>ny</sub><sub>Α</sub>2
Ly2
+
q1
@
Lx,
Ω
D
2
4 Pi2nxΑ2
Lx2
+
4 Pi2nyΑ2
Ly2
+
q1
@
Lx,
Ω
D
2
<sub>+</sub>
<sub>qd</sub>
2
+
2 q1
@
Lx,
Ω
D
2
I
q1
@
Lx,
Ω
D
2
<sub>+</sub>
<sub>qd</sub>
2
M
2
;
d2
@
Lx_,
Ω
_
D
=
4 Pi2<sub>nx</sub><sub>Α</sub>2
Lx2
+
4 Pi2<sub>ny</sub><sub>Α</sub>2
Ly2
+
q2
@
Lx,
Ω
D
2
4 Pi2nxΑ2
Lx2
+
4 Pi2nyΑ2
Ly2
+
q2
@
Lx,
Ω
D
2
<sub>+</sub>
<sub>qd</sub>
2
+
2 q2
@
Lx,
Ω
D
2
I
q2
@
Lx,
Ω
D
2
<sub>+</sub>
<sub>qd</sub>
2
M
2
;
d3
@
Lx_,
Ω
_
D
=
4 Pi2 <sub>nx</sub><sub>Β</sub>2
Lx2
+
4 Pi2<sub>ny</sub><sub>Β</sub>2
Ly2
+
q3
@
Lx,
Ω
D
2
4 Pi2 nxΒ2
Lx2
+
4 Pi2nyΒ2
Ly2
+
q3
@
Lx,
Ω
D
2
<sub>+</sub>
<sub>qd</sub>
2
+
2 q3
@
Lx,
Ω
D
2
I
q3
@
Lx,
Ω
D
2
<sub>+</sub>
<sub>qd</sub>
2
M
2
;
d4
@
Lx_,
Ω
_
D
=
4 Pi2 nxΒ2
Lx2
+
4 Pi2nyΒ2
Ly2
+
q4
@
Lx,
Ω
D
2
4 Pi2 nxΒ2
Lx2
+
4 Pi2nyΒ2
Ly2
+
q4
@
Lx,
Ω
D
2
<sub>+</sub>
<sub>qd</sub>
2
+
2 q4
@
Lx,
Ω
D
2
I
q4
@
Lx,
Ω
D
2
<sub>+</sub>
<sub>qd</sub>
2
M
2
;
H1
@
Lx_,
Ω
_
D
=
f
Α
@
Lx
D
1
-
1
ã
h2 q1@Lx,ΩD2
2 m +EnΗ@LxD-Ef
kb T
+
<sub>1</sub>
+
Nq
-
Nq
1
ã
h2 q1@Lx,ΩD2
2 m +EnΗ@LxD-Ef
kb T
+
<sub>1</sub>
;
H2
@
Lx_,
Ω
_
D
=
1
-
1
ã
h2 q2@Lx,ΩD2
2 m +EnΗ@LxD-Ef
kb T
<sub>+</sub>
<sub>1</sub>
H
1
-
f
Α
@
Lx
D
+
Nq
L
-
Nq f
Α
@
Lx
D
;
H3
@
Lx_,
Ω
_
D
=
1
ã
h2 q3@Lx,ΩD2
2 m +EnΗ@LxD-Ef
kb T
+
<sub>1</sub>
</div>
<span class='text_page_counter'>(4)</span><div class='page_container' data-page=4>
H4
@
Lx_,
Ω
_
D
=
f
Β
@
Lx
D
1
-
1
ã
h2 q4@Lx,ΩD2
2 m +EnΗ@LxD-Ef
kb T
+
<sub>1</sub>
+
Nq
-
Nq
1
ã
h2 q4@Lx,ΩD2
2 m +EnΗ@LxD-Ef
kb T
+
<sub>1</sub>
;
B
@
Lx_,
Ω
_
D
=
HS
@
Lx
D H
d1
@
Lx,
Ω
D
H1
@
Lx,
Ω
D
-
d2
@
Lx,
Ω
D
H2
@
Lx,
Ω
D
+
d3
@
Lx,
Ω
D
H3
@
Lx,
Ω
D
-
d4
@
Lx,
Ω
D
H4
@
Lx,
Ω
DL
;
P
@
Lx_,
Ω
_
D
=
E0
2
2
Ω
â
i=1
2
â
j=1
2
â
n=1
2
â
l=1
2
<sub>dt</sub>
2
<sub>h k</sub>
<sub>Α</sub>
<sub>k</sub>
<sub>Β</sub>
m
2
Lx Ly
ND
@
Lx
D
B
@
Lx,
Ω
D
H
h
Ω -
H
E
Β
@
Lx
D
-
E
Α
@
Lx
DLL
2
<sub>+</sub>
<sub>B</sub>
@
<sub>Lx,</sub>
<sub>Ω</sub>
D
2
;
p1
=
Plot
A9
P
A
162 10
-10
,
Ω
10
15
E
10
12
, P
A
160 10
-10
,
Ω
10
15
E
10
12
,
P
A
158 10
-10
,
Ω
10
15
E
10
12
, P
A
156 10
-10
,
Ω
10
15
E
10
12
,
P
A
154 10
-10
,
Ω
10
15
E
10
12
, P
A
152 10
-10
,
Ω
10
15
E
10
12
,
P
A
150 10
-10
,
Ω
10
15
E
10
12
, P
A
148 10
-10
,
Ω
10
15
E
10
12
,
P
A
146 10
-10
,
Ω
10
15
E
10
12
, P
A
144 10
-10
,
Ω
10
15
E
10
12
,
P
A
142 10
-10
,
Ω
10
15
E
10
12
, P
A
140 10
-10
,
Ω
10
15
E
10
12
,
P
A
138 10
-10
,
Ω
10
15
E
10
12
, P
A
136 10
-10
,
Ω
10
15
E
10
12
=
,
8
Ω
, 1.7 , 2.2
<E
p2
=
Plot
A9
P
A
162 10
-10
,
Ω
10
15
E
10
12
8.10, P
A
160 10
-10
,
Ω
10
15
E
10
12
6.90,
P
A
158 10
-10
,
Ω
10
15
E
10
12
6.00, P
A
156 10
-10
,
Ω
10
15
E
10
12
5.00,
P
A
154 10
-10
,
Ω
10
15
E
10
12
4.30, P
A
152 10
-10
,
Ω
10
15
E
10
12
3.70,
P
A
150 10
-10
,
Ω
10
15
E
10
12
3.20, P
A
148 10
-10
,
Ω
10
15
E
10
12
2.70,
P
A
146 10
-10
,
Ω
10
15
E
10
12
2.30, P
A
144 10
-10
,
Ω
10
15
E
10
12
1.95,
P
A
142 10
-10
,
Ω
10
15
E
10
12
1.66, P
A
140 10
-10
,
Ω
10
15
E
10
12
1.40,
P
A
138 10
-10
,
Ω
10
15
E
10
12
1.19, P
A
136 10
-10
,
Ω
10
15
E
10
12
=
,
8
Ω
, 1.7 , 2.2
<E
</div>
<span class='text_page_counter'>(5)</span><div class='page_container' data-page=5>
<b>FindRootAPA160 10</b> <b>,Ω10</b> <b>E10</b> <b>6.90</b> <b>3.2,8Ω, 1.876<E;</b>
<b>FindRootAPA160 10-10,Ω1015E10126.903.2,8Ω, 2.020<E;</b>
<b>FindRootAPA158 10-10,Ω1015E10126.00</b> <b>3.2,8Ω, 1.869<E;</b>
<b>FindRootAPA158 10-10,Ω1015E10126.003.2,8Ω, 2.022<E;</b>
<b>FindRootAPA156 10-10,Ω1015E10125.00</b> <b>3.2,8Ω, 1.863<E;</b>
<b>FindRootAPA156 10-10,Ω1015E10125.003.2,8Ω, 2.023<E;</b>
<b>FindRootAPA154 10-10,Ω</b>
10
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<b>E10124.30</b> <b>3.2,8Ω, 1.860<E;</b>
<b>FindRootAPA154 10-10,Ω</b>
10
<b>15</b>
<b>E10124.303.2,8Ω, 2.024<E;</b>
<b>FindRootAPA152 10-10,Ω</b>
10
<b>15</b>
<b>E10123.70</b> <b>3.2,8Ω, 1.852<E;</b>
<b>FindRootAPA152 10-10,Ω</b>
10
<b>15</b>
<b>E10123.703.2,8Ω, 2.031<E;</b>
<b>FindRootAPA150 10-10,Ω</b>
10
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<b>E10123.20</b> <b>3.2,8Ω, 1.842<E;</b>
<b>FindRootAPA150 10-10,Ω</b>
10
<b>15</b>
<b>E10123.203.2,8Ω, 2.037<E;</b>
<b>FindRootAPA148 10-10,Ω</b>
10
<b>15</b>
<b>E10122.70</b> <b>3.2,8Ω, 1.834<E;</b>
<b>FindRootAPA148 10-10,Ω</b>
10
<b>15</b>
<b>E10122.703.2,8Ω, 2.039<E;</b>
<b>FindRootAPA146 10-10,Ω</b>
10
<b>15</b>
<b>E10122.30</b> <b>3.2,8Ω, 1.822<E;</b>
<b>FindRootAPA146 10-10,Ω</b>
10
<b>15</b>
<b>E10122.303.2,8Ω, 2.046<E;</b>
<b>FindRootAPA144 10-10,Ω</b>
10
<b>15</b>
<b>E10121.95</b> <b>3.2,8Ω, 1.812<E;</b>
<b>FindRootAPA144 10-10,Ω</b>
10
<b>15</b>
<b>E10121.953.2,8Ω, 2.050<E;</b>
<b>FindRootAPA142 10-10,Ω</b>
10
<b>15</b>
<b>E10121.66</b> <b>3.2,8Ω, 1.798<E;</b>
<b>FindRootAPA142 10-10,Ω</b>
10
<b>15</b>
<b>E10121.663.2,8Ω, 2.057<E;</b>
<b>FindRootAPA140 10-10,Ω</b>
10
<b>15</b>
<b>E10121.40</b> <b>3.2,8Ω, 1.782<E;</b>
<b>FindRootAPA140 10-10,Ω</b>
10
<b>15</b>
<b>E10121.403.2,8Ω, 2.062<E;</b>
<b>xData=9140 10-10, 142 10-10, 144 10-10, 146 10-10, 148 10-10,</b>
<b>150 10-10, 152 10-10, 154 10-10, 156 10-10, 158 10-10, 160 10-10, 162 10-10</b> <b>=</b>
<b>yData=90.37706 1015, 0.33666 1015, 0.30678 1015, 0.28405 1015, 0.26399 1015, 0.24743 1015,</b>
<b>0.23128 1015, 0.21698 1015, 0.20471 1015, 0.19420 1015, 0.18703 1015, 0.181264 1015=</b>
<b>dataToPlot</b> <b>=TransposeB:xData 1010,</b>
<b>h</b>
<b>dt</b>
<b>yData>F</b>
<b>H*ListPlot@dataToPlot ,PlotStyle</b> <b>-></b> <b>,</b>
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<b>PlotStyle®<, PlotRange®99136 10-10, 162 10-10=,80, 0.4<=E</b>
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<b>PlotStyle®, Red<, PlotRange</b> <b>®Automatic</b>
</div>
<span class='text_page_counter'>(6)</span><div class='page_container' data-page=6>
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1.8 1.9 2.0 2.1 2.2
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3
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<span class='text_page_counter'>(7)</span><div class='page_container' data-page=7>
88140, 0.248388<,8142, 0.221775<,8144, 0.202091<,8146, 0.187118<,
8148, 0.173903<,8150, 0.162995<,8152, 0.152356<,8154, 0.142936<,
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</div>
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