Thermodynamics, Statistical Physics, and Quantum Mechanics

68

The same small constantUoccurs inbothterms of Useperturbation

theory tocalculate thechange in theground stateenergy to order

5.44 Relativistic Oscillator (MIT, Moscow

Phys-Tech, Stony Brook (a))

Consider aspinlessparticle in a one-dimensional harmonicoscillatorpoten-

tial:

a) Calculateleadingrelativistic corrections to theground state tofirst

order inperturbationtheory.

b) Consider an anharmonicclassicaloscillatorwith

For whatvalues of will the leading corrections bethe same as in

(a)?

5.45 Spin Interaction (Princeton)

Consider aspin-1/2particle which is bound in a three-dimensional har-
monic oscillator with frequency The ground stateHamiltonian and
spininteraction are

where is aconstant and are thePaulimatrices. Neglect
the spin–orbitinteraction. Useperturbation theory to calculate the change
in the groundstateenergy to order

5.46 Spin–Orbit Interaction (Princeton)

Consider inthreedimensions an electron in aharmonicoscillatorpotential
which is perturbed by thespin–orbitinteraction

PROBLEMS