# 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} }

## 16 Citations

### A new exactly solvable two-dimensional quantum model not amenable to separation of variables

- Physics
- 2010

The supersymmetric intertwining relations with second-order supercharges allow us to investigate a new two-dimensional model which is not amenable to standard separation of variables. The…

### Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics

- Physics
- 2010

Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essen- tially based on supersymmetrical…

### Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force

- Physics
- 2007

The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of…

### Nonlinear supersymmetric quantum mechanics: concepts and realizations

- Mathematics
- 2012

The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is outlined and different…

### Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics

- Physics, Mathematics
- 2009

When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We exa- mine this problem in…

### New two-dimensional quantum models with shape invariance

- Physics
- 2011

Two-dimensional quantum models which obey the property of shape invariance are built in the framework of polynomial two-dimensional supersymmetric quantum mechanics. They are obtained using the…

### Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems

- Physics, Mathematics
- 2013

We investigate a peculiar supersymmetry of the pairs of reflectionless quantum mechanical systems described by $n$-soliton potentials of a general form that depends on $n$ scaling and $n$ translation…

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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…

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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…

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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…

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