Using two one-dimensional particle-in-a-box wavefunctions, X(x) and Y(y) below, show that the product function, X(x)Y(y), is an eigenfunction of the two-dimensional Hamiltonian operator for a particle in a two-dimensional box and determine the eigenvalue. -hz az a2 A = 2m ax2 + dyz 2 X(x) = sin Lx 2 Y(y) = nyny sin Ly Ly