Deformation quantization in the teaching of quantum mechanics

Abstract

We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between classical and quantum mechanics. We demionstrate how it can be used to solve specific problems and clarify its relation to conventional quantization and path integral techniques. We also discuss its recent applications in relativistic quantum field theory.

20 pages

Cited by in corpus (52)

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• Holography from quantum cosmology
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• Deformation quantization of cosmological models
• High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
• The Compton-Schwarzschild correspondence from extended de Broglie relations
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• Generalized Uncertainty Principle Corrections to the Simple Harmonic Oscillator in Phase Space
• Anharmonic quantum mechanical systems do not feature phase space trajectories
• Phase-space representation of Landau and electron coherent states for uniaxially strained graphene
• On infinite walls in deformation quantization
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• Weyl-Wigner-Moyal Formalism for Fermi Classical Systems
• Coherent representation of fields and deformation quantization
• String quantization: Fock vs. LQG Representations
• A new framework for numerical simulations of structure formation
• Deformed phase space in a two dimensional minisuperspace model
• The Weyl-Wigner-Moyal formalism on a discrete phase space. I. A Wigner function for a nonrelativistic particle with spin
• Polymer Quantum Mechanics as a Deformation Quantization
• The Quantum State Of The Universe From Deformation Quantization and Classical-Quantum Correlation
• Induced entanglement entropy of harmonic oscillators in noncommutative phase space
• Towards the deformation quantization of linearized gravity
• Wigner functions, contact interactions, and matching
• Deformation quantization for coupled harmonic oscillators on a general noncommutative space
• Wigner functions for angle and orbital angular momentum: Operators and dynamics
• Quantum-Classical Dynamical Brackets
• On Wigner functions and a damped star product in dissipative phase-space quantum mechanics
• Deformation Quantization of Fermi Fields
• The symbol of a function of an operator
• Deformation quantization of constrained systems: a group averaging approach
• Coherent state quantization of angle, time, and more irregular functions and distributions
• Signature Change by GUP
• Shape invariance in phase space
• Deformation quantization and the tomographic representation of quantum fields
• Quantum and statistical mechanics in open systems: theory and examples
• Signature Change in Noncommutative FRW Cosmology
• Phase Space Quantum Mechanics
• Lindblad Superoperators from Wigner's Phase Space Continuity Equation
• A selection principle in deformation quantization
• Deformation Quantization of Relativistic Particles in Electromagnetic Fields
• Spectrum of the harmonic oscillator in a general noncommutative phase space
• Causal Poisson bracket via deformation quantization
• Deformation Quantization: From Quantum Mechanics to Quantum Field Theory
• A new antisymmetric bilinear map for type-I gauge theories
• Deformation quantization for systems with second-class constraints in deformed fermionic phase space
• Rarita-Schwinger Quantum Free Field Via Deformation Quantization
• The Dirac-Bohm Picture
• Deformation quantization in the teaching of Lie group representations
• Deformation Quantization in Singular Spaces