Stochastic Method for Calculating Wave Functions

A relationship between the Boltzmann transport equation for a point in $3n$-dimensional configuration space executing random motion and the Schrödinger wave equation for $n$ electrons is investigated. It is shown that wave functions and related quantities for the ground and excited states of atomic systems may be calculated with a stochastic computer program by incorporating the Pauli exclusion principle into the stochastic formalism. Stochastic calculations are presented for the ground state of hydrogen and for the ${}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^3{}_{}{}^{}S$ states of helium.