Question

A one-dimensional box of width L contains two spinless particles each of mass m. The interaction between the particles is described by a potential energy V(x₁, x₂) = a\(\delta\)(x₁ - x₂). Calculate the ground state energy to first order in a.

Answer 1

Neglecting the h-potential, we have

Using the results for an infinitely deep potential well, we have

The correction to the ground state energy due to the perturbation is