# Properties of one-dimensional correlated Gaussian wave functions

## Abstract

The properties of a certain class of unsymmetrized one-dimensional correlated Gaussian wave functions-those which are ground-state eigenfunctions of some coupled harmonic-oscillator Hamiltonian-are investigated in detail. It is shown that a properly symmetrized wave function constructed from these may be used to calculate the expectation value E0 of the Hamiltonian appropriate to a system of interacting one-dimensional atoms and that this energy is, to a high degree of accuracy, equal to the value obtained when the unsymmetrized wave function is used. A method is given by which correction terms to E0 may be obtained. In addition, it is found that even though the number of particles be very large, the necessary multivariable integrals may be performed quite simply. © 1966 The American Physical Society.