Thermodynamics, Statistical Physics, and Quantum Mechanics

52 PROBLEMS

5.2 Shallow Square Well II (Stony Brook)

A particle of mass is confined tomove in onedimension by a potential

(seeFigureP.5.2):

Derive theequation for theboundstate.

From the results of part (a), derive an expression for the minimum

value of which will have aboundstate.

Give the expression for theeigenfunction of astatewith positive en-

ergy

Show that theresults of (c) define aphaseshift for thepotential, and

derive anexpression for the phaseshift.

5.3 Attractive Delta Function Potential I (Stony

Brook)

A particle ofmass moves in onedimensionunder the influence of an
attractive deltafunctionpotential at the origin. The Schrödinger equation

a)

b)

c)

d)