The SchrödingerNewton system with selffield coupling
Abstract
We study the SchrödingerNewton (SN) system of equations with the addition of gravitational field energy sourcing—such additional nonlinearity is to be expected from a theory of gravity (like general relativity (GR)), and its appearance in this simplified scalar setting (one of Einstein's precursors to GR) leads to significant changes in the spectrum of the selfgravitating theory. Using an iterative technique, we compare the mass dependence of the ground state energies of both SN and the new, selfsourced system and find that they are dramatically different. The Bohr method approach from old quantization provides a qualitative description of the difference, which comes from the additional nonlinearity introduced in the selfsourced case. In addition to comparison of ground state energies, we calculate the transition energy between the ground state and first excited state to compare emission frequencies between SN and the selfcoupled scalar case.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 March 2015
 DOI:
 10.1088/02649381/32/6/065010
 arXiv:
 arXiv:1501.07537
 Bibcode:
 2015CQGra..32f5010F
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 to appear, Class. Quant. Grav