Remarks on the noncommutative gravitational quantum well

Abstract

A planar phase space having both position and momentum noncommutativity is defined in a more inclusive setting than that considered elsewhere. The dynamics of a particle in a gravitational quantum well in this space is studied. The use of the WKB approximation and the virial theorem enable analytic discussions on the effect of noncommutativity. Consistent results are obtained following either commutative space or noncommutative space descriptions. Comparison with recent experimental data with cold neutrons at Grenoble imposes an upper bound on the noncommutative parameter. Also, our results are compared with a recent numerical analysis of a similar problem. Finally, we provide a noncommutative version of the virial theorem for the case at hand.

Upper bound of the time-space non-commutative parameter from gravitational quantum well experiment

“…Interestingly, the value of the upper bound derived, here, can be shown [18] to be consistent with the results of [23,24].…”

“…In particular, GRANIT experimental data [22], which shows the quantum states of the neutrons trapped in earth's gravitational field, have been used to set an upper bound on the momentum space NC parameters [23,24] by analyzing the gravitational well problem using NC quantum mechanics, where non-commutativity is introduced among the phase-space variables at the Hamiltonian level. Therefore, non-commutativity in the time-space sector, i.e., θ 0i = 0 is not accounted for.…”

Solution of Dirac Equation with the Time-Dependent Linear Potential in Non-Commutative Phase Space

“…In this paper we are interested in non-perturbation investigation of Dirac equation with time-dependent linear potential in non-commutative phase space [32,34,35]. The main purpose of the paper is to construct the timedependent invariant of the Dirac equation with time-dependent linear potential and to obtain, through the Lewis-…”

Hydrogen and muonic hydrogen atomic spectra in non-commutative space-time

“…Here we would like to study the two-body bound state in non-commutative space to explore the differences in the electronic and muonic hydrogen spectrum. There are many studies on the hydrogen atom in the NC space-time [70][71][72][73][74][75][76][77][78][79][80]. However, the effect of NC space on the hydrogen atom at the lowest order is doubtful.…”