About maximally localized states in quantum mechanics

Abstract

We analyze the emergence of a minimal length for a large class of generalized commutation relations, preserving commutation of the position operators and translation invariance as well as rotation invariance (in dimension higher than one). We show that the construction of the maximally localized states based on squeezed states generally fails. Rather, one must resort to a constrained variational principle.

accepted for publication in PRD

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• Modelling Casimir Wormholes in Extended Gravity
• Extended GUP formulation and the role of momentum cut-off
• Casimir-Polder intermolecular forces in minimal length theories
• Influence of GUP corrected Casimir energy on zero tidal force wormholes in modified teleparallel gravity with matter coupling
• Casimir wormhole with GUP correction in extended symmetric teleparallel gravity
• Maximally Localized States in Quantum Mechanics with a Modified Commutation Relation to All Orders
• WKB approximation in deformed space with minimal length and minimal momentum
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• Hawking Radiation Under Generalized Uncertainty Principle
• Heuristic derivation of the Casimir effect from Generalized Uncertainty Principle
• Maximally localized states and quantum corrections of black hole thermodynamics in the framework of a new generalized uncertainty principle
• WKB approximation in deformed space with minimal length
• n-dimensional non-commutative GUP quantization and application to the Bianchi I model
• A framework for nonrelativistic isotropic models based on generalized uncertainty principles
• Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario
• On Dirac theory in the space with deformed Heisenberg algebra. Exact solutions
• Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
• Quantum mechanics on non commutative spaces and squeezed states: a functional approach
• The Fuzzy Sphere: From The Uncertainty Relation To The Stereographic Projection
• Regularization of ${\delta }^{\prime }$ potential in general case of deformed space with minimal length
• Remarks on the quasi-position representation in models of generalized uncertainty principle
• Matter Geometry Coupling and Casimir Wormhole Geometry
• Particle in a cavity in one-dimensional bandlimited quantum mechanics
• Maximally localized states and quantum corrections of black hole thermodynamics in the extreme case with an improved exponential GUP