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Applied quantum mechanics
FINAL EXAMPLE 2
SIMKS
Speed of light in free space
Planck’s constant
Electron charge
Electron mass
Neutron mass
Proton mass
Boltzmann
constant
Permittivity of free space
Permeability of free space
Speed of light in free space
Avagadro’s number
Bohr radius
Inverse finestructure constant
c
2.99792458
10
8
×
m
s
1
–
=
h
6.58211889
10
16
–
×
eV s
=
h
1.054571596
10
34
–
×
J s
=
e
1.602176462
10
19
–
×
C
=
m
0
9.10938188
10
31
–
×
kg
=
m
n
1.67492716
10
27
–
×
=
m
p
1.67262158
10
27
–
×
=
k
B
1.3806503
10
23
–
×
J
K
1
–
=
k
B
8.617342
10
5
–
×
eV
K
1
–
=
ε
0
8.8541878
10
12
–
×
F
m
1
–
=
µ
0
4
π
10
7
–
×
H
m
1
–
=
c
1
ε
0
µ
0
⁄
=
N
A
6.02214199
10
23
×
mol
1
–
=
a
B
0.52917721
10
–
×
10
m
=
a
B
4
πε
0
h
2
m
0
e
2

=
α
1
–
137.0359976
=
α
1
–
4
0
h
c
e
2

=
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View Full Document PROBLEM 1
The timeindependent Schrödinger equation for Hamiltonian
has known orthonormal eigen
functions
such that
where
.
In the presence of a timedependent
change in potential
applied at time
t
> 0 the system evolves in time according to
where
and
are timedependent coefficients.
(a) Show that for time
t
> 0
where
and
.
(30%)
(b)
In firstorder timedependent perturbation theory
is assumed small and
is
approximated by its initial value
.
Show that for time
t
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This note was uploaded on 02/01/2009 for the course EE 539 taught by Professor Levi during the Fall '06 term at USC.
 Fall '06
 Levi

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