A class of partially solvable two-dimensional quantum models with periodic potentials

DOI10.1016/j.nuclphysb.2007.07.010zbMath1151.81011arXiv0706.1344OpenAlexW1979978786MaRDI QIDQ2461151

J. Mateos Guilarte, Mikhail V. Ioffe, Pavel A. Valinevich

Publication date: 26 November 2007

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.1344

zbMATH Keywords

supersymmetry2-dim periodic potentialspartial solvability

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Exactly and quasi-solvable systems arising in quantum theory (81U15)

Related Items (4)

Analytical solution of two-dimensional Scarf II model by means of SUSY methods ⋮ General solution of the two-dimensional intertwining relations for supercharges with hyperbolic (Lorentz) metrics ⋮ Quasi-exactly solvable relativistic soft-core Coulomb models ⋮ New two-dimensional quantum models with shape invariance

Cites Work

• Hidden nonlinear supersymmetry of finite-gap Lamé equation
• Two-dimensional supersymmetry: from SUSY quantum mechanics to integrable classical models
• Exactly solvable two-dimensional complex model with a real spectrum
• Polynomial supersymmetry and dynamical symmetries in quantum mechanics
• Some exact results for mid-band and zero band-gap states of associated Lamé potentials
• Group theoretical properties and band structure of the Lamé Hamiltonian
• New methods for the two-dimensional Schrödinger equation: SUSY-separation of variables and shape invariance
• A SUSY approach for investigation of two-dimensional quantum mechanical systems
• New two-dimensional quantum models partially solvable by the supersymmetrical approach
• Classical integrable two-dimensional models inspired by SUSY quantum mechanics
• On the families of orthogonal polynomials associated to the Razavy potential
• New two-dimensional integrable quantum models from SUSY intertwining
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