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<span class='text_page_counter'>(1)</span><div class='page_container' data-page=1>

Clear

A

T, h, m, kb, chivc, chi0, epxi,

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,

, 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;



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_,

_

D

=

k

Α

2

+

2 m



h

2

H



h

Ω -

h

l

+

En

Η

@

Lx

D

-

En

Α

@

Lx

DL

;



q2

@

Lx_,

_

D

=

k

Α

2

+

2 m



h

2

H



h

Ω +

h

l

-

En

Η

@

Lx

D

+

En

Α

@

Lx

DL

;



q3

@

Lx_,

_

D

=

k

Β

2

<sub>-</sub>

2 m



h

2

H




h

Ω -

h

l

+

En

Η

@

Lx

D

-

En

Β

@

Lx

DL

;



q4

@

Lx_,

_

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_,

_

D

=



4 Pi2<sub>nx</sub><sub>Α</sub>2


Lx2

+



4 Pi2<sub>ny</sub><sub>Α</sub>2


Ly2

+

q1

@

Lx,

D


2


4 Pi2nxΑ2


Lx2

+



4 Pi2nyΑ2


Ly2

+

q1

@

Lx,

D



2

<sub>+</sub>

<sub>qd</sub>

2


+

2 q1

@

Lx,

D



2



I

q1

@

Lx,

D

2

<sub>+</sub>

<sub>qd</sub>

2

M

2


;



d2

@

Lx_,

_

D

=



4 Pi2<sub>nx</sub><sub>Α</sub>2


Lx2

+



4 Pi2<sub>ny</sub><sub>Α</sub>2


Ly2

+

q2

@

Lx,

D


2


4 Pi2nxΑ2


Lx2

+



4 Pi2nyΑ2


Ly2

+

q2

@

Lx,

D



2

<sub>+</sub>

<sub>qd</sub>

2


+

2 q2

@

Lx,

D



2



I

q2

@

Lx,

D

2

<sub>+</sub>

<sub>qd</sub>

2

M

2


;



d3

@

Lx_,

_

D

=



4 Pi2 <sub>nx</sub><sub>Β</sub>2


Lx2

+



4 Pi2<sub>ny</sub><sub>Β</sub>2


Ly2

+

q3

@

Lx,

D


2


4 Pi2 nxΒ2


Lx2

+



4 Pi2nyΒ2


Ly2

+

q3

@

Lx,

D



2

<sub>+</sub>

<sub>qd</sub>

2


+

2 q3

@

Lx,

D



2


I

q3

@

Lx,

D

2

<sub>+</sub>

<sub>qd</sub>

2

M

2


;



d4

@

Lx_,

_

D

=



4 Pi2 nxΒ2


Lx2

+



4 Pi2nyΒ2


Ly2

+

q4

@

Lx,

D


2


4 Pi2 nxΒ2


Lx2

+



4 Pi2nyΒ2


Ly2

+

q4

@

Lx,

D



2

<sub>+</sub>

<sub>qd</sub>

2


+

2 q4

@

Lx,

D



2


I

q4

@

Lx,

D

2

<sub>+</sub>

<sub>qd</sub>

2

M

2

;




H1

@

Lx_,

_

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_,

_

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_,

_

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_,

_

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_,

_

D

=

HS

@

Lx

D H

d1

@

Lx,

D

H1

@

Lx,

D



-

d2

@

Lx,

D

H2

@

Lx,

D

+

d3

@

Lx,

D

H3

@

Lx,

D

-

d4

@

Lx,

D

H4

@

Lx,

DL

;


P

@

Lx_,

_

D

=

E0



2


2

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,

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

,

10

15

E

10

12

, P

A

160 10

-10

,

10

15

E

10

12

,


P

A

158 10

-10

,

10

15

E

10

12

, P

A

156 10

-10

,

10

15

E

10

12

,



P

A

154 10

-10

,

10

15

E

10

12

, P

A

152 10

-10

,

10

15

E

10

12

,


P

A

150 10

-10

,

10

15

E

10

12

, P

A

148 10

-10

,

10

15

E

10

12

,


P

A

146 10

-10

,

10

15

E

10

12

, P

A

144 10

-10

,

10

15

E

10

12

,


P

A

142 10

-10

,

10

15

E

10

12

, P

A

140 10

-10

,

10

15

E

10

12

,



P

A

138 10

-10

,

10

15

E

10

12

, P

A

136 10

-10

,

10

15

E

10

12

=

,

8

, 1.7 , 2.2

<E


p2

=

Plot

A9

P

A

162 10

-10

,

10

15

E

10

12

8.10, P

A

160 10

-10

,

10

15

E

10

12

6.90,



P

A

158 10

-10

,

10

15

E

10

12

6.00, P

A

156 10

-10

,

10

15

E

10

12

5.00,


P

A

154 10

-10

,

10

15

E

10

12

4.30, P

A

152 10

-10

,

10

15

E

10

12

3.70,


P

A

150 10

-10

,

10

15

E

10

12

3.20, P

A

148 10

-10

,

10

15

E

10

12

2.70,


P

A

146 10

-10

,

10

15

E

10

12

2.30, P

A

144 10

-10

,

10

15

E

10

12

1.95,


P

A

142 10

-10

,

10

15

E

10

12

1.66, P

A

140 10

-10

,

10

15

E

10

12

1.40,



P

A

138 10

-10

,

10

15

E

10

12

1.19, P

A

136 10

-10

,

10

15

E

10

12

=

,

8

, 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>Š3.2,8Ω, 1.876<E;</b>
<b>FindRootAPA160 10-10,Ω1015E10126.90Š3.2,8Ω, 2.020<E;</b>
<b>FindRootAPA158 10-10,Ω1015E10126.00</b> <b>Š3.2,8Ω, 1.869<E;</b>
<b>FindRootAPA158 10-10,Ω1015E10126.00Š3.2,8Ω, 2.022<E;</b>
<b>FindRootAPA156 10-10,Ω1015E10125.00</b> <b>Š3.2,8Ω, 1.863<E;</b>
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<b>FindRootAPA144 10-10,Ω</b>

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<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>
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<b>H*ListPlot@dataToPlot ,PlotStyle</b> <b>-></b> <b>,</b>
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</div>
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<b>PlotStyle®, Red<, PlotRange</b> <b>®Automatic</b>


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88140, 0.248388<,8142, 0.221775<,8144, 0.202091<,8146, 0.187118<,


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