Quantum Mechanics: Concepts and Applications · Problem 8.11

Approximation Methods for Stationary States — Nouredine Zettili

Physics — Quantum Mechanics · four-fermions-same-spin-infinite-well

Problem

Consider a system of four noninteracting identical spin

\frac{1}{2}

particles that are in the same spin state

\left|\frac{1}{2}, \frac{1}{2}\right\rangle

and confined to move in a one-dimensional infinite potential well of length

a

V(x) = 0

for

0 < x < a

and

V(x) = \infty

for other values of

x

. Determine the energies and wave functions of the ground state, the first excited state, and the second excited state.