Answer to Question #87278 in Quantum Mechanics for Sridhar

Question

Three Identical spin-half fermions are to be distributed in two non-degenerate distinct energy levels. The number of ways this can be done is.
1)8
2)4
3)3
4)4

Answer 1

Each fermion, having spin one-half, has two independent spin states (say, spin up and spin down with respect to some fixed axis). Because of Pauli principle for fermions, each energy level can accommodate only two particles with oppositely directed spin and total spin zero; there is only one quantum spin state for such two particles. The third particle has to occupy the other energy level, with two spin states (up or down). Thus, the configuration with two particles on the first level and one particle on the second level has two independent states, and, likewise, the configuration with two particles on the second level and one particle on the first level has two independent states. The total number of independent states is, therefore, equal to four.

Answer: 4