Physics 486
Fall 2007
Discussion Problems 7
1) A particle of mass, m, in the potential, V(x) = ½
m
ω
2
x
2
, starts out (at
t
= 0) in
the state
2
2
2
( ,0)
1
2
m
x
m
x
A
x
e
ω
ω

Ψ
=

ℏ
ℏ
, for some constant,
A
.
(a) What is the expectation value of the energy, <E>?
(b) At some later time, T, the wave function is given by:
2
2
2
( ,
)
1
2
m
x
m
x T
B
x
e
ω
ω

Ψ
=
+
ℏ
ℏ
, for some constant,
B
.
What is the smallest possible value of T?
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Physics 486
Fall 2007
2) Based on Griffiths 3.37. The Hamiltonian for a certain three level system in
represented by the matrix
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 Fall '08
 Staff
 Energy, Mass, Quantum Physics, Fundamental physics concepts, later time, A. Ψ

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