Quantum mechanics of a particle in an accelerated frame and the equivalence principle

¹ Department of Physics, West Bengal State University, Barasat - Kolkata 700126, India
² Department of Physical Sciences, Indian Institute of Science Education & Research Kolkata, Mohanpur 741246, Nadia, India
³ Visiting Associate in Inter University Centre for Astronomy & Astrophysics - Pune 411007, India

^(a) sukanta706@gmail.com
^(b) sunandan.gangopadhyay@gmail.com
sunandan@iiserkol.ac.in
sunandan@associates.iucaa.in
^(c) anirban@associates.iucaa.in

Received: 3 September 2017
Accepted: 3 January 2018

Abstract

We study the effect of acceleration of a uniformly accelerated frame on the free-particle dynamics in a quantum domain. Specifically we demonstrate how the behaviour of a free quantum particle, as observed by an observer with uniform acceleration, completely changes from that of a quantum particle immersed in a uniform gravitational field. We also extend our analysis to the simplest noncommutative space scenario to show that while spatial noncommutativity does not affect the quantum particle in a gravitational field, it does alter the energy eigenvalues of a quantum particle as seen from a frame with uniform acceleration.