Thermodynamics, Statistical Physics, and Quantum Mechanics

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where is theangle around the circle. Anelectric field is imposed in the

plane of the circle. Find theperturbedenergylevels up to

5.41 Rotator in Field (Stony Brook)

Consider a rigidbody with moment of inertiaI, which is constrained to

rotate in the and whosemotion isgiven by theSchrödinger equa-

tion

a) Find theeigenfunctions andeigenvalues.

b) Assume therotator has afixed dipole momentpin the plane. An

electric field isapplied to the plane. Find thechanges in theenergy

levels tofirst and secondorder in the field.

5.42 Finite Size of Nucleus (Maryland, Michigan

State, Princeton, Stony Brook)

Regard the nucleus of charge Z as a sphere of radius with a uniform

charge density. Assumethat where is theBohrradius of the

hydrogen atom.

Derive an expression for theelectrostaticpotential between the

nucleus and the electrons in the atom. If is the

potential from a point charge, find the difference

due to the size of the nucleus.

Assume one electron isbound to thenucleus in thelowestbound

state. What is its wavefunction whencalculatedusing the potential

from apoint nucleus?

Use first-order perturbationtheory toderive an expression for the

change in the ground stateenergy of theelectron due to the finite

size of the nucleus.

a)

b)

c)

5.43 U and Perturbation (Princeton)

A particle is moving inthe three-dimensionalharmonicoscillatorwith po-
tentialenergy A weakperturbation is applied:

QUANTUM MECHANICS