(a) Write down the Hamiltonian for two noninteracting identical particles in the infinit...

(a) Write down the Hamiltonian for two noninteracting identical particles in the infinite square well. Verify that the fermion ground state given in Example 5.1 is an eigenfunction of H, with the appropriate eigenvalue.

(b) Find the next two excited states (beyond the ones in Example 5.1)—wave functions and energies—for each of the three cases (distinguishable, identical bosons, identical fermions).

Example 5.1

Suppose we have two noninteracting—they pass right through one another ... never mind how you would set this up in practice!—particles, both of mass in, in the infinite square well (Section 2.2). The one-particle states are