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

H. S. Vieira; V. B. Bezerra; C. R. Muniz; M. S. Cunha; H. R. Christiansen

doi:10.1016/j.physletb.2020.135712

paper

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

arXiv:2003.13377 · doi:10.1016/j.physletb.2020.135712

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, $0 \leq p \leq 2$ . We investigate the minimum value of the scale factor with respect to the maximum value of the probability density.

6 pages, 9 figures