PHYS 271 2009: Problem Set 3
Due Friday, Feb. 13, 2009 at the start of class.
Problem sets are to be done individually. Be sure to put your name and student number on your assignment;
problem sets without a
name will not be graded
.
For all problems, be sure to fully explain what you are doing using words
.
1. A particle in onedimension moves in some unknown potential energy
V
(
x
)
. One ±nds that it is described by a wavefunction
ψ
(
x,t
)=
e

iωt
cos(
kx
)
where
ω
=
Ak
2
+
B
. Here,
A
and
B
are constants. You can assume that this is a good wavefunction, meaning it is a solution to
the Schrodinger equation.
(a) What units must the constant
A
have? What units must the constant
B
have?
(b) How does the mass of the electron depend on the constants
A
and
B
?
(c) Find an expression for the potential energy
V
(
x
)
in terms of the constants
A
and
B
.
2. For this problem, we will consider an electron living in one spatial dimension which is restricted to the region between
x
=0
and
x
=
L
. The following is a wavefunction that could describe our particle:
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 Winter '10
 AashishClark
 Quantum Physics, wavefunction ψa

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