Post-Newtonian corrections to Schr\"odinger equations in gravitational fields
Abstract
In this paper we extend the WKB-like `non-relativistic' expansion of the minimally coupled Klein--Gordon equation after Kiefer and Singh [1], L\"ammerzahl [2] and Giulini and Gro{\ss}ardt [3] to arbitrary order in , leading to Schr\"odinger equations describing a quantum particle in a general gravitational field, and compare the results with canonical quantisation of a free particle in curved spacetime, following Wajima et al. [4]. Furthermore, using a more operator-algebraic approach, the Klein--Gordon equation and the canonical quantisation method are shown to lead to the same results for some special terms in the Hamiltonian describing a single particle in a general stationary spacetime, without any `non-relativistic' expansion.
Keywords
Cite
@article{arxiv.1812.05181,
title = {Post-Newtonian corrections to Schr\"odinger equations in gravitational fields},
author = {Philip K. Schwartz and Domenico Giulini},
journal= {arXiv preprint arXiv:1812.05181},
year = {2019}
}
Comments
28 pages, published in Classical and Quantum Gravity. v2: corrected typos, revised section 2 and beginning of section 3, extended discussion of results in section 3. v3: corrected reference [10]