Class of solutions of the Wheeler-DeWitt equation with ordering parameter

Abstract

In this letter, we discuss the Wheeler-DeWitt equation with an ordering parameter in the Friedmann-Robertson-Walker universe. The solutions when the universe was very small and at the end of the expansion are obtained in terms of Bessel and Heun functions, respectively. We also obtain a boundary condition which should be satisfied by the ordering parameter, namely, p ≤ 1. We investigate the minimum value of the scale factor with respect to the maximum value of the probability density.