Physics 486
Fall 2007
Discussion Problems 10
1).
Two masses, m
1
and m
2
, which are restricted to moving in a plane, are connected
by a massless rod of length R to form a rigid rotator.
Notes: one can turn this into
a one particle problem by using a reduced mass
μ
=m
1
m
2
/(m
1
+m
2
).
Also, this system
has only 1 degree of freedom, which can be chosen to be either the arc length S or
the rotational angle
ϕ
, where S=R
ϕ
.
(a)
Write down the Schrödinger equation for this system.
(b)
Determine the unnormalized eigenstates of the SEQ in part (a).
(c) By imposing the requirement that the wavefunction must be singlevalued,
determine the energy eigenvalues for the rigid rotator:
(d) Show that the eigenstates of the Hamiltonian, which you determined in (b), are
also eigenstates of the angular momentum operator L
z
.
What does this tell you
about the operators H and L
z
?
Verify that H and L
z
commute.
What are the
measurable values of the angular momentum for this system?
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 Fall '08
 Staff
 Angular Momentum, Mass, Quantum Physics

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