Question

Find parts a and b.

Consider the three-dimensional cubic well V = {(0 if 0<x<a, 0<y<a, 0<z<a), (infinity otherwise).

The stationary states are psi^(0) (x, Y, z) = (2/a)^(3/2)sin(npix/a)sin(npiy/a) sin(npiz/a), where nx, ny , and nz are integers.

The corresponding allowed energies are E^0 = (((pi^2)(hbar^2))/2m(a^2))(nx^2+ny^2+nz^2).

Now let us introduce perturbation V={(V0 if 0<x<(a/2), 0<y<(a/2)), (0 otherwise)

a) Find the first-order correction to the ground state energy.

b) Find the first-order correction to the first excited state.

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