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. -h2 H = 2m 0x2 + dy2 2 X (x ) = sin Lx Lx 2 nyny Y (y ) = sin Ly Ly