7. Consider two noninteracting particles in a 1D simple harmonic
oscillator (SHO) potential, which has 1-particle spatial
wavefunctions ψ n ( x), where n = 0, 1, 2, … (we ignore spin by
assuming both particles have the same spin quantum number or are
spin 0). These wavefunctions are normalized to 1 and satisfy ψ n *
( x)ψ m ( x)dx −∞ ∞ ∫ = 0 when n ≠ m , i.e., they are orthogonal.
The energies are !ω0...