Quantum Newtonian cosmology and the biconfluent Heun functions
General Relativity and Quantum Cosmology
2015-09-16 v2 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1502.03071,
title = {Quantum Newtonian cosmology and the biconfluent Heun functions},
author = {H. S. Vieira and V. B. Bezerra},
journal= {arXiv preprint arXiv:1502.03071},
year = {2015}
}
Comments
15 pages, 2 figures