Ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable models with quadratic complex interaction. II: Three-dimensional model

DOI10.3842/SIGMA.2022.005zbMath1484.81031arXiv2010.15276OpenAlexW4205483851MaRDI QIDQ2073672

Ian Marquette, Christiane Quesne

Publication date: 3 February 2022

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.15276

zbMATH Keywords

complex potentialsLie algebrasquantum mechanicsLie superalgebraspseudo-Hermiticity

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Linear symmetric and selfadjoint operators (unbounded) (47B25) Applications of Lie (super)algebras to physics, etc. (17B81) Groups and algebras in quantum theory and relations with integrable systems (81R12) Supersymmetry and quantum mechanics (81Q60) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items (1)

Dynamical symmetry algebras of two superintegrable two-dimensional systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exactly solvable two-dimensional complex model with a real spectrum
• Quasi-Hermitian operators in quantum mechanics and the variational principle
• Real eigenspectra in non-Hermitian multidimensional Hamiltonians
• Ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable models with quadratic complex interaction. I: two-dimensional model
• Equidistance of the complex two-dimensional anharmonic oscillator spectrum: the exact solution
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• New methods for the two-dimensional Schrödinger equation: SUSY-separation of variables and shape invariance
• Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians
• Exactly solvable nonseparable and nondiagonalizable two-dimensional model with quadratic complex interaction
• Three-dimensional shape invariant non-separable model with equidistant spectrum
• On Dirac's New Method of Field Quantization
• Quantum complex Hénon-Heiles potentials

This page was built for publication: Ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable models with quadratic complex interaction. II: Three-dimensional model