The eigenvalue equation for a 1-D Hamilton function in deformation quantization

DOI10.1016/j.physleta.2012.05.009zbMath1266.53084arXiv1106.1358OpenAlexW2962854437MaRDI QIDQ2376241

Jaromir Tosiek

Publication date: 21 June 2013

Published in: Physics Letters. A, Geometric Methods in Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.1358

zbMATH Keywords

Wigner function\(\ast\)-eigenvalue equation

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Geometry and quantization, symplectic methods (81S10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Deformation quantization, star products (53D55) Stochastic quantization (81S20)

Related Items (4)

The Wentzel–Kramers–Brillouin approximation method applied to the Wigner function ⋮ States in the Hilbert space formulation and in the phase space formulation of quantum mechanics ⋮ Formal series of generalized functions and their application to deformation quantization ⋮ Wigner functions on non-standard symplectic vector spaces

Cites Work

• Wigner measures in noncommutative quantum mechanics
• Fedosov manifolds
• A simple geometrical construction of deformation quantization
• Formal solutions of stargenvalue equations
• Admissible states in quantum phase space
• The Narcowich-Wigner spectrum of a pure state
• Geometrical origin of the \(\ast\)-product in the Fedosov formalism
• On the Quantum Correction For Thermodynamic Equilibrium
• The Formulation of Quantum Mechanics in terms of Ensemble in Phase Space
• On the principles of elementary quantum mechanics
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