E = 13E0. This degeneracy arises from interchanging nx and ny (which is the
same as interchanging the x and y axes), so the probability distributions in the
two cases are not very different. However, consider the state with E = 50E0, for
which there are three sets of quantum numbers: nx
= 7, ny
= 1; nx
= 1, ny
= 7;
and nx
= 5, ny
= 5. The first two sets of quantum numbers result from the interchange
of nx and ny and so have similar probability distributions, but the third
represents a very different state of motion, as shown in Figure 5.19. The level
at E = 13E0 is said to be two-fold degenerate, while the level at E = 50E0 is
three-fold degenerate; we could also say that one level has a degeneracy of 2,
while the other has a degeneracy of 3.
E = 13E0. This degeneracy arises from interchanging nx and ny (which is thesame as interchanging the x and y axes), so the probability distributions in thetwo cases are not very different. However, consider the state with E = 50E0, forwhich there are three sets of quantum numbers: nx= 7, ny= 1; nx= 1, ny= 7;and nx= 5, ny= 5. The first two sets of quantum numbers result from the interchangeof nx and ny and so have similar probability distributions, but the thirdrepresents a very different state of motion, as shown in Figure 5.19. The levelat E = 13E0 is said to be two-fold degenerate, while the level at E = 50E0 isthree-fold degenerate; we could also say that one level has a degeneracy of 2,while the other has a degeneracy of 3.
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