## 23 Citations

### Two-dimensional magnetic Schrödinger equations, Darboux transformations and solutions of associated auxiliary equations

- Mathematics
- 2012

We extend the formalism of Darboux transformations to magnetic Schrodinger equations in two dimensions. The partner potentials associated with the Darboux transformation are obtained in explicit form…

### Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation

- Mathematics
- 2002

### Multidimensional integrable Schrödinger operators with matrix potential

- Mathematics
- 1999

The Schrodinger operators with matrix rational potential, which are D-integrable, i.e., can be intertwined with the pure Laplacian, are investigated. Corresponding potentials are uniquely determined…

### Multidimensional Integrable Schrödinger Operators With Matrix Potential February 18 , 1999

- Mathematics
- 1999

The Schrödinger operators with matrix rational potential, which are D-integrable, i.e. can be intertwined with the pure Laplacian, are investigated. Corresponding potentials are uniquely determined…

### Separation of Coupled Systems of Schrodinger Equations by Darboux Transformations

- Mathematics
- 2012

Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper, we introduce a novel application of these…

### Darboux Transformations for Energy-Dependent Potentials and the Klein–Gordon Equation

- Mathematics, Physics
- 2013

We construct explicit Darboux transformations for a generalized Schrödinger-type equation with energy-dependent potential, a special case of which is the stationary Klein–Gordon equation. Our results…

### Darboux Transformations of Bispectral Quantum Integrable Systems

- Mathematics, Physics
- 1999

We present an approach to higher-dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators.…

### Darboux transformations for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix

- Physics, Mathematics
- 2012

We construct a Darboux transformation for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix. Our transformation is based on the two-dimensional supersymmetry formalism for the…

### Nonsingular brane solutions via the Darboux transformation

- Mathematics, Physics
- 2005

We consider the Darboux transformation as a method of construction of exact nonsingular solutions describing the three-dimensional brane that interacts with five-dimensional gravity and the bulk…

### Loughborough University Institutional Repository Multidimensional integrable Schrodinger operators with matrix potential

- Mathematics
- 2018

The Schrödinger operators with matrix rational potential, which are D-integrable, i.e. can be intertwined with the pure Laplacian, are investigated. Corresponding potentials are uniquely determined…

## References

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- MathematicsBulletin of the Australian Mathematical Society
- 1994

We define the notion of Darboux integrability for linear second order partial differential operators, . We then build on certain geometric results of E. Vessiot related to the theory of Monge…

### New quasi-exactly solvable Hamiltonians in two dimensions

- Mathematics
- 1994

Quasi-exactly solvable Schrödinger operators have the remarkable property that a part of their spectrum can be computed by algebraic methods. Such operators lie in the enveloping algebra of a…

### Real Lie algebras of differential operators and quasi-exactly solvable potentials

- MathematicsPhilosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 1996

We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie…

### Supersymmetry and Morse theory

- Physics
- 1982

It is shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian. Some of the implications of modern ideas in mathematics for…

### Quasi-Exactly Solvable Models in Quantum Mechanics

- Mathematics, Physics
- 1994

QUASI-EXACT SOLVABILITY-WHAT DOES THAT MEAN? Introduction Completely algebraizable spectral problems The quartic oscillator The sextic oscillator Non-perturbative effects in an explicit form and…

### Quasi-exact Solvability

- Mathematics
- 1994

This paper surveys recent work on quasi-exactly solvable Schrr odinger operators and Lie algebras of diierential operators.

### The factorization method

- Mathematics
- 1951

The factorization method is an operational procedure which enables us to answer, in a direct manner, questions about eigenvalue problems which are of importance to physicists. The underlying idea is…