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.

Latex, 17 pages, Title changed, minor modifications, 3 new references added, To appear in Phys. Rev. D

References in corpus (2)

• Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces
• Constraint on Quantum Gravitational Well in Noncommutative Space

Cited by in corpus (11)

• Lie algebraic Noncommutative Gravity
• Berry Phase in the Gravitational Quantum Well and the Seiberg-Witten map
• Deformed Reissner--Nordstrom solutions in noncommutative gravity
• Time-Space Noncommutativity in Gravitational Quantum Well scenario
• Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves
• Centrifugal quantum states of neutrons
• Modified Newton's law, braneworlds, and the gravitational quantum well
• Particle-like solutions to classical noncommutative gauge theory
• The quantum N-body problem with a minimal length
• On the question of deconfinement in noncommutative Schwinger Model
• Theories on noncommutative spaces and deformed symmetries