To investigate our model, which consists of two electrons confined to a one-dimensional external potential, we utilized the method of exact diagonalization to solve the two-body Schrödinger equation. We build a two-particle wave function from a set of single-particle functions. The representation of the one-body Hamiltonian's eigenstates on a discrete grid offers us the flexibility to select the external potential of our choice, and it also fits the interpolated potential very effectively.