A particle moves in a potential well given by U(x, y, z) = 0 for –L/2 < x < L/2, 0 < y < L, and 0 < z < L, and U = ∞ outside these ranges.

(a) Write an expression for the ground-state wave function for this particle.

(b) How do the allowed energies compare with those for a box having U = 0 for 0 < x < L, rather than for –L/2 < x < L/2?