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Unformatted text preview: 24. Using Eq. 4020 (see also problem 27 in Chapter 40) we ﬁnd that the lowest four levels of the rectangular
corral (with this speciﬁc “aspect ratio”) are nondegenerate, with energies E1,1 = 1.25, E1,2 = 2.00,
E1,3 = 3.25, and E2,1 = 4.25 (all of these understood to be in “units” of h2 /8mL2 ). Therefore, obeying
the Pauli principle, we have
Eground = 2E1,1 + 2E1,2 + 2E1,3 + E2,1 = 2(1.25) + 2(2.00) + 2(3.25) + 4.25
which means (putting the “unit” factor back in) that the lowest possible energy of the system is Eground =
17.25(h2 /8mL2 ). ...
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 Fall '08
 SPRUNGER
 Physics

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