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.

••• Show that the allowed energies of a mass M confined in a three-dimensional rectangular rigid box with sides a, b, and c are

where the three quantum numbers nx, ny, nz are any three positive integers . [Hint: Use separation of variables, and seek a solution of the form ψ = X(x)Y(y)Z(z). Note that by setting a = b = c, one obtains the cubical box of Example 8.2.]