One-Dimensional, Many-Body Calculation with a Correlated Gaussian Wave Function

A two-parameter many-body correlated Gaussian wave function is used to calculate the expectation value of the Hamiltonian for $N$ one-dimensional particles interacting through the one-dimensional analog of an atomic potential. Using a potential equal to four times the Slater-Kirkwood He-He potential, we calculate the optimum average interparticle separation, the ground-state energy, and the velocity of sound of the system as a function of particle mass. It is found that the correlated Gaussian always gives an improvement in energy compared with an uncorrelated Gaussian.