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26 Nov 2019
2 .6.4 Consider an electron in a three-dimensional cubic box ofside length Lz . The walls of the box are
presumed to correspond to infinitely high potentials.
(i) Find an expression for the allowed energies of the electron inthis box. Express your result in
terms of the lowest allowed energy, E18 , of a particle in aone-dimensional box.
(ii) State the energies and describe the form of the wavefunctionsfor the 4 lowest energy states.
(iii) Are any of these states degenerate? If so, say which, andalso give the degeneracy associated
with any of the eigenenergies you have found that are degenerate.
2 .6.4 Consider an electron in a three-dimensional cubic box ofside length Lz . The walls of the box are
presumed to correspond to infinitely high potentials.
(i) Find an expression for the allowed energies of the electron inthis box. Express your result in
terms of the lowest allowed energy, E18 , of a particle in aone-dimensional box.
(ii) State the energies and describe the form of the wavefunctionsfor the 4 lowest energy states.
(iii) Are any of these states degenerate? If so, say which, andalso give the degeneracy associated
with any of the eigenenergies you have found that are degenerate.
