p41_027 - 2 , 1 , 1 = 6( h 2 / 8 mL 2 ). Each of these...

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27. In terms of the quantum numbers n x , n y ,and n z , the single-particle energy levels are given by E n x ,n y ,n z = h 2 8 mL 2 ( n 2 x + n 2 y + n 2 z ) . The lowest single-particle level corresponds to n x =1 , n y =1 ,and n z =1andis E 1 , 1 , 1 =3( h 2 / 8 mL 2 ). There are two electrons with this energy, one with spin up and one with spin down. The next lowest single-particle level is three-fold degenerate in the three integer quantum numbers. The energy is E 1 , 1 , 2 = E 1 , 2 , 1
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Unformatted text preview: 2 , 1 , 1 = 6( h 2 / 8 mL 2 ). Each of these states can be occupied by a spin up and a spin down electron, so six electrons in all can occupy the states. This completes the assignment of the eight electrons to single-particle states. The ground state energy of the system is E gr = (2)(3)( h 2 / 8 mL 2 ) + (6)(6)( h 2 / 8 mL 2 ) = 42( h 2 / 8 mL 2 )....
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