ECE 306
Homework Set #5
Spring 2005
(Due 12 noon, Wednesday, March 2, 2005)
1.
A beam of noninteracting electrons propagates along the xaxis in an infinite,
onedimensional space with V(x) = 0.
a.
Many measurements of linear momentum and total energy are made. In 25% of
the measurements an electron is found moving to the right with energy E
1
, and in
75% of the measurements an electron is found moving to the left with energy E
2
.
Construct a nonnormalized wave function for the electron beam,
Ψ
(x, t) in terms
of E
1
, E
2
and fundamental constants, that will account for the stated results.
b.
Is
Ψ
(x, t) an eigen function of p
x
and/or H?
c.
Does
Ψ
(x, t) satisfy the timeindependent Schroedinger’s equation, energy eigen
value equation, both equations or neither. Explain.
d.
What is the wave function of an electron after a measurement of its energy yields
the result E
2
.
2.
A particle of mass m, traveling along the xaxis in a region of constant potential
energy has the following wave function:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '05
 TANG
 Gate, Fundamental physics concepts, wave function, eigen function

Click to edit the document details