Thermodynamics, Statistical Physics, and Quantum Mechanics

250 SOLUTIONS

5.6 Transmission Through a Delta Function Potential

(Michigan State, MIT, Princeton)

On the left the particle has an incident intensity, which we set equal to

unity, and a reflected amplitude R. On the right the transmitted amplitude

is denoted by T.

At the point we match the value of on both sides. We match

the derivative according to an expression such as (S.5.3.3) with

This yields two equations for T and R which can be solved for T:

5.7 Delta Function in a Box (MIT)

a) In the absence of the delta functionpotential, the states with odd parity

are

These states have zero amplitude at the site of the delta function
and are unaffected by it. So, the states with odd parity have the same
eigenfunction and eigenvalues as when the delta function is absent.

b), c) For a delta function potential without a box, the bound states have
a wave function of (see Problem 5.3). In the box we expect to
have similar exponentials, except that the wave function must vanish at
the edges of the box The states which do this are