Post-Newtonian corrections to Schrödinger equations in gravitational fields

authored by

Philip K. Schwartz, Domenico Giulini

Abstract

In this paper we extend the WKB-like 'non-relativistic' expansion of the minimally coupled Klein-Gordon equation after (Kiefer and Singh 1991 Phys. Rev. D 44 1067-76; Lammerzahl 1995 Phys. Lett. A 203 12-7; Giulini and Großardt 2012 Class. Quantum Grav. 29 215010) to arbitrary order in c ^-1, leading to Schrödinger 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 1997 Phys. Rev. D 55 1964-70). 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.

Organisation(s)

CRC 1227 Designed Quantum States of Matter (DQ-mat)
Institute of Theoretical Physics

External Organisation(s)

University of Bremen
Center of Applied Space Technology and Microgravity (ZARM)

Type

Article

Journal

Classical and Quantum Gravity

Volume

36

ISSN

0264-9381

Publication date

09.05.2019

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

Electronic version(s)

https://doi.org/10.48550/arXiv.1812.05181 (Access: Open)
https://doi.org/10.1088/1361-6382/ab0fbd (Access: Open)
https://doi.org/10.15488/5103 (Access: Open)
https://doi.org/10.1088/1361-6382/ab5633 (Access: Open)