Minimal Length and Bouncing Particle Spectrum

Abstract

In this paper we study the effects of the Generalized Uncertainty Principle (GUP) on the spectrum of a particle that is bouncing vertically and elastically on a smooth reflecting floor in the Earth's gravitational field (a quantum bouncer). We calculate energy levels and corresponding wave functions of this system in terms of the GUP parameter. We compare the outcomes of our study with the results obtained from elementary quantum mechanics. A potential application of the present study is discussed finally.

10 pages, 1 figure, to appear in Europhysics Letters

References in corpus (26)

• Noncommutative Field Theory
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Background Independent Quantum Gravity: A Status Report
• Quantum gravity and minimum length
• A Generalized Uncertainty Principle in Quantum Gravity
• The Generalized Uncertainty Principle and Black Hole Remnants
• Loop Quantum Gravity
• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle
• The algebraic structure of the generalized uncertainty principle
• Spin Foam Models for Quantum Gravity
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Lectures on Loop Quantum Gravity
• Phenomenological Implications of the Generalized Uncertainty Principle
• Measurement of quantum states of neutrons in the Earth's gravitational field
• Generalized Uncertainty Principle, Extra-dimensions and Holography
• Black Hole Remnants and Dark Matter
• Study of the neutron quantum states in the gravity field
• Deformed Special Relativity as an effective flat limit of quantum gravity
• Some Consequences of the Generalised Uncertainty Principle: Statistical Mechanical, Cosmological, and Varying Speed of Light
• Some Aspects of Minimal Length Quantum Mechanics
• Some Aspects of Planck Scale Quantum Optics
• A class of GUP solutions in deformed quantum mechanics
• On the modification of Hamiltonians' spectrum in gravitational quantum mechanics
• Generalized Uncertainty Principle and Quantum Electrodynamics
• Spontaneous emission of graviton by a quantum bouncer

Cited by in corpus (39)

• Minimal Length Scale Scenarios for Quantum Gravity
• Generalized Uncertainty Principle: Approaches and Applications
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum
• Minimal length, maximal momentum and Hilbert space representation of quantum mechanics
• Review on Generalized Uncertainty Principle
• The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications
• New Approach to Nonperturbative Quantum Mechanics with Minimal Length Uncertainty
• Deformed Heisenberg algebra with minimal length and equivalence principle
• 30 years in: Quo vadis generalized uncertainty principle?
• Semiclassical corrections to black hole entropy and the generalized uncertainty principle
• New generalized uncertainty principle from the doubly special relativity
• Minimal length, maximal momentum and the entropic force law
• Position and Momentum Uncertainties of the Normal and Inverted Harmonic Oscillators under the Minimal Length Uncertainty Relation
• Electroweak Theory with a Minimal Length
• Singular inverse square potential in coordinate space with a minimal length
• Generalized Uncertainty Principle and the Ramsauer-Townsend Effect
• Kratzer's molecular potential in quantum mechanics with a generalized uncertainty principle
• One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum
• Harmonic oscillator with minimal length, minimal momentum, and maximal momentum uncertainties in SUSYQM framework
• Deformed Heisenberg algebra and minimal length
• Emergent universe in theories with natural UV cutoffs
• Minimal Length and the Quantum Bouncer: A Nonperturbative Study
• The Minimal Length and the Quantum Partition Functions
• Exact Ultra Cold Neutrons' Energy Spectrum in Gravitational Quantum Mechanics
• The Constraints and Spectra of a Deformed Quantum Mechanics
• Coherent States in Gravitational Quantum Mechanics
• GRASIAN: Towards the first demonstration of gravitational quantum states of atoms with a cryogenic hydrogen beam
• Generalized uncertainty principle and thermostatistics: a semiclassical approach
• EGUP corrected thermodynamics of RN-AdS black hole with quintessence matter
• Deformed Gazeau-Klauder Schrödinger-Cat States with Modified Commutation Relations
• Relation of deformed nonlinear algebras with linear ones
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
• $\lambda {\varphi }^4$ Kink and sine-Gordon Soliton in the GUP Framework
• A Note on Coherent States with Quantum Gravity Effects
• Regularization of ${\delta }^{\prime }$ potential in general case of deformed space with minimal length
• Quantum-Corrected Thermodynamics of Conformal Weyl Gravity Black Holes: GUP Effects and Phase Transitions
• Particle in a cavity in one-dimensional bandlimited quantum mechanics