  We obtain the exact solution of the Schr\"odinger 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.
