Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun's differential equation

DOI10.3792/pjaa.89.69zbMath1278.34099OpenAlexW2043689877WikidataQ115219885 ScholiaQ115219885MaRDI QIDQ372585

Masato Wakayama

Publication date: 9 October 2013

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pja/1370004861

zbMATH Keywords

multiplicity of eigenvaluesoscillator representationlowest eigenvalueHeun's differential equationnon-commutative harmonic oscillatorsRiemann's scheme

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Entire and meromorphic solutions to ordinary differential equations in the complex domain (34M05) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (6)

Determinant Expressions of Constraint Polynomials and the Spectrum of the Asymmetric Quantum Rabi Model ⋮ 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 ⋮ On the essential spectrum of certain non-commutative oscillators ⋮ Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-commutative harmonic oscillators and the connection problem for the Heun differential equation
• Spectral theory of non-commutative harmonic oscillators: an introduction
• On the spectral zeta function for the noncommutative harmonic oscillator
• On the spectrum of certain noncommutative harmonic oscillators
• On the spectrum of certain non-commutative harmonic oscillators and semiclassical analysis
• Zeta functions for the spectrum of the non-commutative harmonic oscillators
• Oscillator representations and systems of ordinary differential equations
• MULTIPLICITY OF THE LOWEST EIGENVALUE OF NON-COMMUTATIVE HARMONIC OSCILLATORS
• Non-commutative harmonic oscillators-II
• The Dicke-type crossings among eigenvalues of differential operators in a class of non-commutative oscillators
• THE HEAT SEMIGROUP AND KERNEL ASSOCIATED WITH CERTAIN NON-COMMUTATIVE HARMONIC OSCILLATORS
• 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
• A variation of multiple $L$-values arising from the spectral zeta function of the non-commutative harmonic oscillator
• On the essential spectrum of certain non-commutative oscillators
• Non-commutative harmonic oscillators and Fuchsian ordinary differential operators

This page was built for publication: Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun's differential equation