Best Qphysics Book
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7
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8 ; "" " + '
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7 7 7 7
# * < P # P
!
9 ; + 6' 8 . * " * * * " + " ' 4* " :
+ " # P 4' ' " ' ' " K # "" " ' "P # "" " + ' "P
? !@A 7 Æ@ A # @AP # * P # * P @ ; < < " 7 / ; @A ' " < # 4' ' B
7 " 0 2 ; "" " ' F
D
% @A 7 % # ' ' < " P ' ' " ' ' ' # ' ' < '
7
+ F"F * " ' + * 8 I < " 6< A 5 ' " 8 "8 " 4' ' " 7 7 G ' G # "" ' P 6U ' + 8
77
7
7 " * " ; "" " ' 6U ' '
8 ; "" " + '
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@A
7
F % @A 7 @A
@
M
% A
@A 7
; % ' + 7
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# " " ' @A 7 @+A F - @+A
# " '
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. 7 '
@A 7 F -
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# ' % % @A 7
(
F%
*
!!
; " " % ' ' "
7 " - !7 C ; * @A 7 F +7
M
4 ' Æ " 7 6) " " 8 ; ¼ @A 7 '
+ 7
@
M
% A
64 " ' ¼ 8
Energy e ikx
+ Re-ikx
Te ik’x
E V0 transmitted
incident wave
V(x)
reflected
0 0
x
& Æ ' ' ' " " " $ # ' ( * ' " ' + '
" * 6 " ' ' ! ' 8 - % - 7 F 7'
( 7 (
!'
- !% % - %- 7 ¼ I"+ "+ J 7 I"+ ' J
. ' ( " # "
+ @ A 7 + @ F A
@+ F + A 7 @+ + A
Æ 7 ' 7F 7
+
+
+ F + + + F +
# ' - @A 7
( F
¼
¼ ¼
¼
*
' " + 6 4 1 . J! " 7
7
+
+
+ F +
64 ' Æ " Æ 7 " C ' " 8 - ' ' '
# 7 " 7
!++ @+ F + A
# 2 ' C Æ "" C 6 B @ 78 " "" 7 + 7 + 6 8 "" + 7 6 ! * 8 A A $
# " ' ' ' % ) % @A 7
* +
%
* **
!*
4" @A 7 F
¼ ¼ @A 7 F -
@A 7 '
' - !7 ! - - ! % ! - *
Aeik’x + Be-ik’x ikx
e
-ikx
+ Re
Energy
transmitted
reflected
0
Teikx E
incident wave
x V(x)
-V 0 0
- & Æ # ' ' + ' " # , '! C 6 B @ 8
7 "
'
7
@+ + A @ + A
F + A @ + A "@+
++ @ + A ++
@
+ A
++
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( J ! ' . % * ! ! " $ "" " "" " C J * < - *A + 7
!
+ 7 7
@
% A
M
F
%
M
&
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A A# : ! $
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'
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M
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- ' 2
@A 7 @+A F - @+A +7
@ F % A
' ' 9 ( 9 ! ' Æ
M
!&
Energy
0
Aeikx + Be-ikx
C1eκx
C3e −κx
x E
V(x)
-V 0 0
6 B @ 8 ' - " * % ! !! # % 6( * 8
. 7 @+A+
@ F % A
@ F % A 7 M M M
@ F % A 7 F% M
!!
. 7 @+A+
@ F % A M
F %
7
( ' ' " ' ( ( E$ F # 6 8 ' ' 7 ' - ' ' '
!)
f(E)
Potential Well Bound States 5 4 3 2 1 0 -1 -2 -3 -4 -5
sqrt tan "-cot"
-20
-15
-10
-5
0
E (hbar**2/2ma**2)
7 - ' A A' :
# / " ' ,
*
)* % @ A 7 + F%
* **
4" @A 7 F
@A 7 F - @A 7 '
' " + ' ; " +7
M
'
- " .7
@%
M
A
Energy
e
ikx
Aeκx +Be−κx
-ikx
+ Re
Te ikx
V(x)
V0
transmitted
reflected
E
incident wave
0
0
x
6 " 8 ' " ' " +
".
! ! ' 7
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7
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7
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+
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F
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*
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% Æ
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(
' .7
*
M
' " " ' # 2 ' " 7 = ' ' # ' 7 " Æ "
Energy
e
0
e−κx
κx
0 x
E V(x)
'
# ' " + 7 5 ! ' + 6 @ @ 8
7
%
7
7
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M
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u(x)
1D Molecule
-4
-2
0
2
V(x) 4 u0(x) u1(x)
x
' < " ' @9 % / : " 6 ' 8 " 9 : G - ' " " ' % 7 @ ' A@ A@ *A G
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%
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+7
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%
M +
@+A
! " ' $7 7 ! ! -
!
+
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@+A + - " ' $7 7 + '
'*
Energy Bands 2
cos(phi)
1 cos(phi) E
0 -1 -2 0
5
10
k (/A)
" ' + "
'
' + " " 6 8 "
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7 7 '
M + @+ F + A + @+ F + A
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)* % @ A 7 +
%
* **
4" F
@A 7
¼ ¼ @A 7 F -
@A 7 '
' ' 6" ' ' ' 8 # ' ' + ' " 9 ( 2 ' 9 7 ' ( ' ' ¼ ¼ ' 7 F - ¼
¼
"+' 7 "+ "+ - ¼ ¼ + ' 7 -
+ ¼ + 7 ' F + ¼ - 7 '
+
+
')
7 ' ( ' ' " ' ' " " ¼ "+ 7 "+
+ F + + + 7 ' + F + + "+
+
¼ ¼ F 7 F -
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¼
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+
¼ "+ -
+
¼
F
¼
+
¼
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+ + +
+
¼
¼
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'
¼
+
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@
+ A
@ + A
+
¼ "
¼ F
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# " (
F + + + + + + " @ + A F " @ + A 7 ' ! + + + + " 7 ' @ + A + + % &
7 '
+
¼
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¼
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' 7
¼
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