Thermodynamics, Statistical Physics, and Quantum Mechanics

QUANTUM MECHANICS 313

a) The wave functions on theleft and right of the origin are

where and are the amplitudesof the reflected andtransmittedwaves.

Matching thewavefunction and itsslope at gives twoequations:

These two equations are solved to obtain and :

b) The particlecurrents are thevelocitiestimes theintensities. Theveloc-

ities are on theleft and on the right:

The last expression equals thecurrent ofthe incomingparticle.

5.63 Repulsive Square Well (Colorado)

a) If the radial part of thewavefunction is thendefine
SinceRis well behaved at in thislimit. The function
obeys thefollowing equation for