Thermodynamics, Statistical Physics, and Quantum Mechanics

71

WKB

5.53 Bouncing Ball (Moscow Phys-Tech, Chicago)

A ball ofmass acted on byuniformgravity (let be theacceleration

of gravity)bounces up and down elastically off afloor.Take thefloor to

be at the zero of potential energy. Working inthe WKB approximation,

compute the quantized energylevels of thebouncingball system.

5.54 Truncated Harmonic Oscillator (Tennessee)

A truncatedharmonicoscillator in one dimension has the potential

a) Use WKB to estimate the energies of theboundstates.

b) Find the conditionthatthere isonly one boundstate: it should de-

pend on and

5.55 Stretched Harmonic Oscillator (Tennessee)

Use WKB in one dimension tocalculate the eigenvalues ofa particle of
mass in thefollowing potential(seeFigureP.5.55):

QUANTUM MECHANICS