VERIFIED NUMERICAL COMPUTATIONS FOR EIGENVALUES OF NON-COMMUTATIVE HARMONIC OSCILLATORS

DOI10.1081/NFA-120014756zbMath1016.65056OpenAlexW2085913252MaRDI QIDQ4787845

Masato Wakayama, Mitsuhiro T. Nakao, Kaori Nagatou

Publication date: 14 April 2003

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/nfa-120014756

zbMATH Keywords

error estimatesHamiltonianeigenfunctionsinterval arithmeticelliptic eigenvalue problemsnon-commutative harmonic oscillatorsmultiple eigenvaluesnumerical enclosure methodminimum-maximum principlerounding arithmetic

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of operator theory in the physical sciences (47N50) General theory of ordinary differential operators (47E05) General methods in interval analysis (65G40) Algorithms with automatic result verification (65G20) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

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Numerical verification method for infinite dimensional eigenvalue problems, Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun's differential equation, Covering families of the asymmetric quantum Rabi model: \(\eta\)-shifted non-commutative harmonic oscillators, Non-commutative harmonic oscillators and related problems, On the spectrum of certain noncommutative harmonic oscillators, On the essential spectrum of certain non-commutative oscillators, Non-commutative harmonic oscillators and the connection problem for the Heun differential equation, On the spectral zeta function for the noncommutative harmonic oscillator, On the spectrum of certain non-commutative harmonic oscillators and semiclassical analysis, Non-commutative Harmonic Oscillators, Zeta functions for the spectrum of the non-commutative harmonic oscillators, Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing

Uses Software

• PROFIL/BIAS

Cites Work

• PROFIL/BIAS - A fast interval library
• A numerical method to verify the elliptic eigenvalue problems including a uniqueness property
• Numerical verifications for eigenvalues of second-order elliptic operators
• Oscillator representations and systems of ordinary differential equations
• Non-commutative harmonic oscillators-II
• An Approach to The Numerical Verification of Solutions for Nonlinear Elliptic Problems With Local Uniqueness
• Non-commutative harmonic oscillators-I