Quantum Newtonian cosmology and the biconfluent Heun functions

Abstract

We obtain the exact solution of the Schrödinger equation for a particle (galaxy) moving in a Newtonian universe with a cosmological constant, which is given in terms of the biconfluent Heun functions. The first six Heun polynomials of the biconfluent function are written explicitly. The energy spectrum which resembles the one corresponding to the isotropic harmonic oscillator is also obtained. The wave functions as well as the energy levels codify the role played by the cosmological constant.