# Darboux transformations in integral and differential forms for generalized Schroedinger equations

## Abstract

The Darboux transformation operator technique is applied to the generalized Schroedinger equation with a position-dependent effective mass and with linearly energy-dependent potentials. Intertwining operators are obtained in an explicit form and used for constructing generalized Darboux transformations. An interrelation is established between the differential and integral transformation operators. It is shown how to construct the quantum well potentials in nanoelectronic with a given spectrum.

- Authors:

- Joint Institute for Nuclear Research (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22043882

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Atomic Nuclei

- Additional Journal Information:
- Journal Volume: 74; Journal Issue: 7; Other Information: Copyright (c) 2011 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7788

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; EFFECTIVE MASS; ENERGY DEPENDENCE; INTEGRAL TRANSFORMATIONS; INTEGRALS; POTENTIALS; QUANTUM OPERATORS; QUANTUM WELLS; SCHROEDINGER EQUATION

### Citation Formats

```
Suzko, A. A., E-mail: suzko@jinr.ru, and Velicheva, E. P.
```*Darboux transformations in integral and differential forms for generalized Schroedinger equations*. United States: N. p., 2011.
Web. doi:10.1134/S1063778811060287.

```
Suzko, A. A., E-mail: suzko@jinr.ru, & Velicheva, E. P.
```*Darboux transformations in integral and differential forms for generalized Schroedinger equations*. United States. doi:10.1134/S1063778811060287.

```
Suzko, A. A., E-mail: suzko@jinr.ru, and Velicheva, E. P. Fri .
"Darboux transformations in integral and differential forms for generalized Schroedinger equations". United States. doi:10.1134/S1063778811060287.
```

```
@article{osti_22043882,
```

title = {Darboux transformations in integral and differential forms for generalized Schroedinger equations},

author = {Suzko, A. A., E-mail: suzko@jinr.ru and Velicheva, E. P.},

abstractNote = {The Darboux transformation operator technique is applied to the generalized Schroedinger equation with a position-dependent effective mass and with linearly energy-dependent potentials. Intertwining operators are obtained in an explicit form and used for constructing generalized Darboux transformations. An interrelation is established between the differential and integral transformation operators. It is shown how to construct the quantum well potentials in nanoelectronic with a given spectrum.},

doi = {10.1134/S1063778811060287},

journal = {Physics of Atomic Nuclei},

issn = {1063-7788},

number = 7,

volume = 74,

place = {United States},

year = {2011},

month = {7}

}

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