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arXiv · 1812.05181

Post-Newtonian corrections to Schr\"odinger equations in gravitational fields

Philip K. Schwartz·Domenico Giulini
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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 $c^{-1}$, 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.

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Philip K. Schwartz, Domenico Giulini. 2018-12-12. Post-Newtonian corrections to Schr\"odinger equations in gravitational fields. https://doi.org/10.1088/1361-6382%2Fab0fbd

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