The Schrödinger-Newton system with self-field coupling
Abstract
We study the Schrödinger-Newton (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 self-gravitating theory. Using an iterative technique, we compare the mass dependence of the ground state energies of both SN and the new, self-sourced 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 self-sourced 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 self-coupled scalar case.
- Publication:
-
Classical and Quantum Gravity
- Pub Date:
- March 2015
- DOI:
- 10.1088/0264-9381/32/6/065010
- arXiv:
- arXiv:1501.07537
- Bibcode:
- 2015CQGra..32f5010F
- Keywords:
-
- Schrödinger-Newton;
- self-energy;
- nonlinear quantum mechanics;
- scalar gravity;
- General Relativity and Quantum Cosmology
- E-Print:
- to appear, Class. Quant. Grav