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3. Consider a particle in a three-dimensional cubic box. a. Calculate the energy for this box, using the Hamiltonian operator, when the particle is in the energy state described by 'I'1,2,3. Where: nxTIX nyIty nzTIZ Unxnynz = ( Z sin ( ax ay -12 sin (a dy ()Z sin az b. Are the following wavefunctions eigenfunctions of the Hamiltonian? If yes, what is the eigenvalue? W = 17 (41,2,3 - 1'3.1.2) W = 1 -V2.2.2 4. Consider a free particle of mass, m, moving in two dimensions, x and y. The potential for the system is: V = 00 for - 00