A particle is confined to a two-dimensional box defined by the following boundary conditions: U(x,y) = 0 for –L/2 ≤ x ≤ L/2 and –3L/2 ≤ y v 3L/2; and U(x,y) = ∞ elsewhere.

(a) Determine the energies of the lowest three bound states. Are any of these states degenerate?

(b) Identify the lowest doubly degenerate bound state by appropriate quantum numbers and determine its energy.