A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials
@article{Ioffe2007ACO, title={A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials}, author={Mikhail V. Ioffe and J. M. Mateos Guilarte and P. A. Valinevich}, journal={Nuclear Physics}, year={2007}, volume={790}, pages={414-431} }
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References
SHOWING 1-10 OF 68 REFERENCES
New two-dimensional quantum models partially solvable by the supersymmetrical approach
- Physics
- 2005
New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via repeated use of the first-order supersymmetrical transformations with intermediate constant unitary…
Exactly solvable two-dimensional complex model with a real spectrum
- Physics, Mathematics
- 2005
Using supersymmetric intertwining relations of the second order in derivatives, we construct a two-dimensional quantum model with a complex potential for which all energy levels and the corresponding…
New two-dimensional integrable quantum models from SUSY intertwining
- Mathematics
- 2006
Supersymmetrical intertwining relations of second order in the derivatives are investigated for the case of supercharges with deformed hyperbolic metric gik = diag(1, − a2). Several classes of…
A SUSY approach for investigation of two-dimensional quantum mechanical systems*
- Physics
- 2004
Different ways to incorporate two-dimensional systems which are not amenable to separation of variables treatment into the framework of supersymmetrical quantum mechanics (SUSY QM) are analysed. In…
Periodic potentials and supersymmetry
- Physics, Mathematics
- 2004
We review the current status of one-dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can…
Two-dimensional supersymmetry : From SUSY quantum mechanics to integrable classical models
- Physics
- 2006
CLASSICAL INTEGRABLE TWO-DIMENSIONAL MODELS INSPIRED BY SUSY QUANTUM MECHANICS
- Mathematics, Physics
- 1998
A class of integrable two-dimensional (2D) classical systems with integrals of motion of fourth order in momenta is obtained from the quantum analogues with the help of deformed SUSY algebra. With…
New solvable and quasi exactly solvable periodic potentials
- Physics
- 1999
Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specif- ically, the…
New methods for the two-dimensional Schrödinger equation: SUSY-separation of variables and shape invariance
- Physics, Mathematics
- 2002
Two new methods for the investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. The first one—SUSY-separation of variables—is…
Three-dimensional exactly solvable model of electron movement in the periodic separable Lame potential
- Physics
- 2006
One-gap and two-gap separable Lame potentials are studied in detail. For onedimensional case we construct the dispersion relation graph E(k) and for threedimensional case we construct the Fermi…