Thermodynamics, Statistical Physics, and Quantum Mechanics

254 SOLUTIONS

If both electrons are in the spin state (spin up), then the spin part of the

wave function is symmetric under exchange of coordinates. Therefore,

the orbital part has to be antisymmetric, and both particles cannot be in

the state. Instead, the lowest energy occurs when one electron is in

the state and the other is in the state:

b) The probabilitythatboth are in one half, say the left side, is

Three integrals must be evaluated:

The result is rather small. Naturally, it is much more favorable to have one
particle on each side of the box.