Squeezed coherent states for gravitational well in noncommutative space

Abstract

Gravitational well is a widely used system for the verification of the quantum weak equivalence principle (WEP). We have studied the quantum gravitational well (GW) under the shed of noncommutative (NC) space so that the results can be utilized for testing the validity of WEP in NC-space. To keep our study widely usable, we have considered both position-position and momentum-momentum noncommutativity. Since coherent state (CS) structure provides a natural bridging between the classical and quantum domain descriptions, the quantum domain validity of purely classical phenomena like free-fall under gravity might be verified with the help of CS. We have constructed CS with the aid of a Lewis-Riesenfeld phase space invariant operator. From the uncertainty relations deduced from the expectation values of the observables, we have shown that the solutions of the time-dependent Schrödinger equation are squeezed-coherent states.

arXiv admin note: substantial text overlap with arXiv:2006.11252

References in corpus (10)

• The Confrontation between General Relativity and Experiment
• Quantum Test of the Universality of Free Fall
• Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity
• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• Proposal for a Quantum Test of the Weak Equivalence Principle with Entangled Atomic Species
• Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
• Time-Space Noncommutativity in Gravitational Quantum Well scenario
• Probing noncommutative theories with quantum optical experiments
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Maxwell's equations and Lorentz force in doubly special relativity

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• Tuning the separability in noncommutative space