# Question

The treatment of a particle in a one-dimensional box can be extended to a rectangular box of dimensions Lx, Ly, and Lz, yielding the following expression for energy:

The three quantum numbers nx, ny, and nz independently can assume only integer values. a. Determine the energies of the three lowest levels, assuming that the box is cubic. b. Describe the degeneracies of all the levels that correspond to quantum numbers having values of 1 or 2. How will these degeneracies change in a box where Lx ≠ Ly ≠ Lz?

The three quantum numbers nx, ny, and nz independently can assume only integer values. a. Determine the energies of the three lowest levels, assuming that the box is cubic. b. Describe the degeneracies of all the levels that correspond to quantum numbers having values of 1 or 2. How will these degeneracies change in a box where Lx ≠ Ly ≠ Lz?

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