The wave function for a particle in a 2-D bbx is given by: =xy (a) Prove that whenever the Hamiltonian, H, can be written as the sum of two parts, namely Hx and Hy, the eigenvalue equation H^=E can be separated into two eigenvalue equations of H^xx=Exx and H^yy=Eyy. Relate the eigenvalues of operators Hx,Hy and H. (10 marks) (b) Assuming that the sides of the box are equal, (i) write the expression for the allowed energy of this system. (ii) construct a table of nx,ny with energies and the degeneracy of the respective level for the quantum numbers ranging from 1 to 3 . (iii) determine the number of state and energy level