Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing

DOI10.1016/j.jmaa.2014.01.005zbMath1315.34090arXiv1304.5578OpenAlexW2050513831MaRDI QIDQ2338882

Itaru Sasaki, Fumio Hiroshima

Publication date: 27 March 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.5578

zbMATH Keywords

multiplicitycrossingnon-commutative harmonic oscillatorthe lowest eigenvalueno crossing

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General theory of ordinary differential operators (47E05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (5)

Covering families of the asymmetric quantum Rabi model: \(\eta\)-shifted non-commutative harmonic oscillators ⋮ Apéry-like numbers for non-commutative harmonic oscillators and automorphic integrals ⋮ Non-commutative harmonic oscillators and related problems ⋮ Number Theoretic Study in Quantum Interactions ⋮ Symmetry of asymmetric quantum Rabi models

Cites Work

• Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun's differential equation
• Spectral theory of non-commutative harmonic oscillators: an introduction
• On the spectral zeta function for the noncommutative harmonic oscillator
• Oscillator representations and systems of ordinary differential equations
• MULTIPLICITY OF THE LOWEST EIGENVALUE OF NON-COMMUTATIVE HARMONIC OSCILLATORS
• Non-commutative harmonic oscillators-II
• Non-commutative harmonic oscillators-I
• ON THE SPECTRUM AND THE LOWEST EIGENVALUE OF CERTAIN NON-COMMUTATIVE HARMONIC OSCILLATORS
• VERIFIED NUMERICAL COMPUTATIONS FOR EIGENVALUES OF NON-COMMUTATIVE HARMONIC OSCILLATORS
• Invariant Cones and Uniqueness of the Ground State for Fermion Systems
• Non-commutative harmonic oscillators and Fuchsian ordinary differential operators

This page was built for publication: Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing