Exact continuity equation in a space with minimal length

Abstract

We derive continuity equation and exact expression for flow probability density in a space with arbitrary deformed algebra leading to minimal length. In coordinate representation the flow probability density is presented as infinite series over parameter of deformation which in momentum representation can be casted into exact closed form determined by deformed kinetic energy. The flow probability density is calculated explicitly for plane wave and for superposition of two plane waves.

References in corpus (31)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• A Generalized Uncertainty Principle in Quantum Gravity
• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• Phenomenological Implications of the Generalized Uncertainty Principle
• Dirac oscillator with nonzero minimal uncertainty in position
• On Quantum Mechanics on Noncommutative Quantum Phase Space
• Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator
• Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length
• Harmonic oscillator with minimal length uncertainty relations and ladder operators
• Exact solutions of the (2+1) Dimensional Dirac equation in a constant magnetic field in the presence of a minimal length
• One dimensional Coulomb-like problem in deformed space with minimal length
• On noncommutative isotropic harmonic oscillator
• Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework
• On Noncommutative Geometric Regularisation
• Noncommutative 3D harmonic oscillator
• More on a SUSYQM approach to the harmonic oscillator with nonzero minimal uncertainties in position and/or momentum
• Can we measure structures to a precision better than the Planck length?
• Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background
• Scattering problem in deformed space with minimal length
• Noncommutative oscillator, symmetry and Landau problem
• Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space
• On the (2+1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty
• Orbital magnetic moment of the electron in the hydrogen atom in deformed space with minimal length
• Deformed Heisenberg algebra and minimal length
• Effect of coordinate noncommutativity on the mass of a particle in a uniform field and the equivalence principle
• Quantum phase transitions of the Dirac oscillator in a minimal length scenario
• Exactly solvable problems in the momentum space with a minimum uncertainty in position
• One-dimensional Coulomb-like problem in general case of deformed space with minimal length
• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• Relation of deformed nonlinear algebras with linear ones
• Exact solutions for two-body problems in 1D deformed space with minimal length