PHYSICS 4455 — QUANTUM MECHANICS
Problem Set 10 — due 12
/
2
/
2005, 5pm in D)r. Schmittmann’s office.
1.
Angular momentum and its commutators – part of every physicist’s rate of passage!
Confirm Liboff Eq. (9.8) and (9.13).
Do Liboff Problems 9.4 (takes just a few minutes), 9.7 (all of it!) and 9.11 (only parts a
and c). Show every step explicitly.
2.
The isotropic harmonic oscillator in two dimensions.
A nonrelativistic, structureless particle of mass
M
is confined by a harmonic oscillator
potential of the form
V
(
x
,
y
)=
1
2
M
ω
2
(
x
2
+
y
2
)
The following sequence of steps takes you through the solution of the associated,
twodimensional Schrödinger equation. The notation follows the class notes.
(i) Write down the stationary Schrödinger equation for this problem, using
twodimensional polar coordinates
ρ
and
φ
. Show that
Ĥ
,
L
z
=
0 and reduce the
eigenvalue problem to the radial differential equation for
R
m
(ρ)
.
(ii) Examine this differential equation in the limit of
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 Spring '09
 Mucciolo
 mechanics, Cartesian Coordinate System, Angular Momentum, Momentum, Eigenvalue, eigenvector and eigenspace, Polar coordinate system

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