Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.

•• Consider a particle in a rigid rectangular box with sides a and b = a/2. Using the result (8.102) (Problem 1), find the lowest six energy levels with their quantum numbers and degeneracies.

Problem 1

•• Consider a particle of mass M in a two-dimensional, rigid rectangular box with sides a and b. Using the method of separation of variables, find the allowed energies and wave functions for this particle. In particular, show that the allowed energies are identified by two integers nx and ny and have the form

Your analysis will be very similar to that given in Section 8.3; the main purposes of this problem are that you go through that analysis yourself and understand how it generalizes to the case of a rectangle with unequal sides.