A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

Expand and apply to (S.5.23.4):

Either the state is zero or So

Similarly,

For and since the only solution is

We knew that was real, but now we have

so

5.24 Triplet Square Well (Stony Brook)

Since the two spins are parallel, they are in a spin triplet state with
and The spin eigenfunction has even parity. The two-electron
wave function is written as an orbital part times the spin part.
The total wave function must have odd parity. Since the spin has even
parity, the orbital part must have odd parity: Since

QUANTUM MECHANICS 269