Quantum Mechanics Solution Manual 

© Leon van Dommelen 

A.28.1 Solution wkba
Question:
Use the equation
to find the WKB approximation for the energy levels of a particle stuck in a pipe of chapter 3.5.5. The potential is zero inside the pipe, given by 0
In this case, the WKB approximation produces the exact result, since the classical momentum really is constant. If there was a force field in the pipe, the solution would only be approximate.
Answer:
Substituting in , 0 and ,
and squaring both sides, the energy is found as . That is the same result as in chapter 3.5.5, but obtained in a much easier way.