Quantum Mechanics - Spin

Let  represent the state of an electron with spin up and  the state of an electron with spin down. Valid spin eigenfunctions for a triplet state of a two-electron atom include which of the following?



A. I only
B. II only
C. III only
D. I and III
E. II and III

GR0177 #82)

Solution:

Singlet state is anti-symmetric: ψ(1,2) = −ψ(2,1)
Triplet state is symmetric: ψ(1,2) = ψ(2,1)

  is symmetric, because



  is antisymmetric, because


  is symmetric, because


Thus, II is singlet state, I and III are triplet state.

Answer: D