For the case in exercise 4, consider a two-particle potential of the Coulomb ( \(\propto 1 / r)\) type. Write explicitly the first six nontrivial terms (those having an occupation number change in the twoparticle operator in the Hamiltonian), in the occupation number basis.

Data From Exercise 4:-

Consider five bosons with a one-body potential that can be approximated as harmonic oscillator. Write the wave function expansion in terms of harmonic oscillator states with \(n \leq 3\).