PHYSICAL CONSTANTS:
8
.
11
)
(
=
Si
r
ε
F/cm
10
854
.
8
14
0
−
×
=
ε
k
B
T
=
25.8meV
(300 K)
Js
10
05
.
1
34
−
×
=
π
2
=
h
q
=
1.60
"
10
#
19
C
E
Ryd
=
e
4
m
0
2(4
"#
0
!
)
2
=
13.6 eV
1 eV =1.60
"
10
-19
J
LATTICES
R
=
n
a
+
m
b
+
p
c
K
=
h
A
+
k
B
+
l
C
A
=
2
"
b
#
c
a
$
(
b
#
c
)
K
"
R
=
2
#
m
QUANTUM MECHANICS
E
=
!
"
=
2
#
!
f
p
=
m
*
v
=
!
q
=
2
"
!
#
2
/
≥
Δ
Δ
p
x
ˆ
H
"
=
i
!
d
dt
"
"
#
(
x
,
t
)
=
$
(
x
)
e
%
i
#
t
ˆ
p
"
=
#
i
!
$
"
"
k
(
x
)
=
e
+
i
k
#
x
ˆ
p
"
k
=
p
"
k
=
!
k
"
k
ˆ
x
"
=
x
"
"
x
0
(
x
)
=
#
(
x
$
x
0
)
ˆ
x
"
x
0
=
x
0
"
x
0
1
=
"
"
=
"
*
"
#
d
3
x
P
(
r
)
=
"
*
(
r
)
"
(
r
)
=
"
(
r
)
2
A
=
"
ˆ
A
"
=
"
*
ˆ
A
"
#
d
3
x
ˆ
H
=
"
!
2
2
m
#
2
+
U
(
ˆ
x
)
if
ˆ
A
= (
ˆ
A
T
)
*
then eigenvalues of
ˆ
A
are real, and
"
*
(
ˆ
A
"
)
d
3
x
=
#
(
ˆ
A
"
*
)
"
d
3
x
#
ˆ
H
"
#
=
E
"
#
=
!
#"
#

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