In which of the following cases would you expect degeneracy of the first excited state? Hint: Make sure to consider all three dimensions

a. A neutral helium atom initially in its ground state in a magnetic field.
b. A particle trapped inside a sphere of radius R.
c. A particle trapped inside a three dimensional box of lengths L1 > L2 > L3.
d. Identical particles, with one in an infinite square-well potential and the other in a finite square-well potential with walls of potential V0 high but of the same width as the infinite potential well.


b.
In all three dimensions the lengths of the "box" are the same, therefore the energies of the first excited state in each dimension are the same. The state is degenerate.

Physics & Space Science

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Physics & Space Science