Self-adjointness of the operators in Wigner’s commutation relations

DOI10.1063/1.529860zbMath0780.46040OpenAlexW2012797871MaRDI QIDQ4030965

Y. Ohnuki, Shuji Watanabe

Publication date: 1 April 1993

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529860

zbMATH Keywords

spectraself-adjointnessFourier transformationintegral transformationsrigged Hilbert space techniquesessential selfadjointness of the position operatorsgeneralized eigenfunctions of the momentum operatorNelson's theorem on analytic vectorsquantum mechanical one-dimensional harmonic oscillatorspectral representation of the momentum operatorWigner communication relation

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Spectrum, resolvent (47A10) Commutators, derivations, elementary operators, etc. (47B47) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Applications of selfadjoint operator algebras to physics (46L60) Applications of functional analysis in quantum physics (46N50) Commutation relations and statistics as related to quantum mechanics (general) (81S05) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

Related Items (6)

An embedding theorem of Sobolev type for an operator with singularity ⋮ Many-body Wigner quantum systems ⋮ Sobolev type theorems for an operator with singularity ⋮ THE EXPLICIT SOLUTIONS TO THE TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH THE SINGULAR POTENTIALS AND ⋮ The explicit solution of a diffusion equation with singularity ⋮ SUPERCONFORMAL QUANTUM MECHANICS VIA WIGNER–HEISENBERG ALGEBRA

Cites Work

• A harmonic oscillator system with the generalized commutation relations
• Elementary Particles and the Principle of Reciprocity
• Quantized Field Theories and the Principle of Reciprocity
• Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?
• A Note on the Quantum Rule of the Harmonic Oscillator

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