Thermodynamics, Statistical Physics, and Quantum Mechanics

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5.56 Ramp Potential (Tennessee)

Use WKB in one dimension to find theeigenvalues of aparticle ofmass
in thepotential where

5.57 Charge and Plane (Stony Brook)

A particlemoving in onedimensionfeels thepotential

(Thispotentialwould be appropriate for an electronmoving in the presence
of a uniformlychargedsheet whereCis the transparency of the sheet.)

Using the WKB approximation,find theenergyspectrum, for

this one-dimensionalproblem for all for

Find the energyspectrum,

Derive an equationthatdescribes the energies for even wavefunc-

tions for anarbitraryvalue ofC.What can you say about theenergies

for odd wavefunctions?

a)

b)

c)

PROBLEMS