Two-dimensional Noncommutative Gravitational Quantum Well

Abstract

In this paper we consider two kinds of noncommutative space-time commutation relations in two-dimensional configuration space and feature the absolute value of the minimal length from the generalized uncertainty relations associated to the particular commutation relations. We study the problem of the two-dimensional gravitational quantum well in the new Hermitian variables and confront the experimental results for the first lowest energy state of the neutrons in the Earth's gravitational field to estimate the upper bounds on the noncommutativity parameters. The absolute value of the minimum length is smaller than a few nanometers.

12 pages

References in corpus (6)

• Minimal Length Uncertainty Relation and gravitational quantum well
• Remarks on the Noncommutative Gravitational Quantum Well
• Time-Space Noncommutativity in Gravitational Quantum Well scenario
• PT-symmetric noncommutative spaces with minimal volume uncertainty relations
• Modification of Schrödinger-Newton equation due to braneworld models with minimal length
• Minimal areas from q-deformed oscillator algebras

Cited by in corpus (12)

• Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space
• Minimal and maximal lengths from position-dependent noncommutativity
• Heat flow and noncommutative quantum mechanics in phase-space
• On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field
• Gravitational Quantum Well as an Effective Quantum Heat Engine
• Position-dependent mass in strong quantum gravitational background fields
• The damped harmonic oscillator at the classical limit of the Snyder-de Sitter space
• Squeezed coherent states for gravitational well in noncommutative space
• Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space
• Tuning the separability in noncommutative space
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation
• Hilbert space representation of maximal length and minimal momentum uncertainties