Thermodynamics, Statistical Physics, and Quantum Mechanics

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5.33 Linear Potential II (MIT, Tennessee)

A particle ofmass moves in onedimension inthe righthalf-space. It has

a potential energy given by

whereFis a positive real constant. Usevariationalmethods toobtain an

estimate for the ground stateenergy. How does thewavefunctionbehave

in the limits or

5.34 Return of Combined Potential (Tennessee)

A particle ofmass moves in onedimension according to thepotential

where and areboth constants.

a) Show that the wavefunction must vanish at so that aparticle

on the right of the originnever gets to theleft.

b) Use variational methods to estimate theenergy of the ground state.

5.35 Quartic in Three Dimensions (Tennessee)

A particle of mass is bound in threedimensions by thequarticpotential

Use variationalmethods to estimate theenergy of theground

state.

5.3 6 Halved Harmonic Oscillator (Stony Brook,

Chicago (b), Princeton (b))

Consider a particle ofmass moving inone dimension (see FigureP.5.36)

in a potential

PROBLEMS