Reconstruction of potentials in quantum dots and other small symmetric structures

Kira V. Khmelnytskaya; Tetyana V. Torchynska

doi:10.1002/mma.1218

Reconstruction of potentials in quantum dots and other small symmetric structures

Kira V. Khmelnytskaya, Tetyana V. Torchynska

Escuela Superior de Física y Matemáticas (ESFM)

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

A method for reconstructing symmetric potentials of Schrödinger operators from a finite set of eigenvalues is presented. The method combines the approach developed by Rundell and Coworkers (SIAM Monographs on Mathematical Modeling and Computation. SIAM: Philadelphia, PA; (1997)) for solving inverse Sturm-Liouville problems with a recent result by Kravchenko (Complex Variables and Elliptic Equations 2008; 53(8):775-789) giving accurate solutions of direct problems. Our construction allows one to recover the potential in situations of great importance in studying nanostructures including quantum dots when only a very limited number of eigenvalues (3-4) obtained experimentally is available.

Original language	English
Pages (from-to)	469-472
Number of pages	4
Journal	Mathematical Methods in the Applied Sciences
Volume	33
Issue number	4
DOIs	https://doi.org/10.1002/mma.1218
State	Published - 15 Mar 2010

Keywords

Inverse problem
Quantum dot
Schrödinger equation

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10.1002/mma.1218

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title = "Reconstruction of potentials in quantum dots and other small symmetric structures",

abstract = "A method for reconstructing symmetric potentials of Schr{\"o}dinger operators from a finite set of eigenvalues is presented. The method combines the approach developed by Rundell and Coworkers (SIAM Monographs on Mathematical Modeling and Computation. SIAM: Philadelphia, PA; (1997)) for solving inverse Sturm-Liouville problems with a recent result by Kravchenko (Complex Variables and Elliptic Equations 2008; 53(8):775-789) giving accurate solutions of direct problems. Our construction allows one to recover the potential in situations of great importance in studying nanostructures including quantum dots when only a very limited number of eigenvalues (3-4) obtained experimentally is available.",

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AU - Khmelnytskaya, Kira V.

AU - Torchynska, Tetyana V.

PY - 2010/3/15

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N2 - A method for reconstructing symmetric potentials of Schrödinger operators from a finite set of eigenvalues is presented. The method combines the approach developed by Rundell and Coworkers (SIAM Monographs on Mathematical Modeling and Computation. SIAM: Philadelphia, PA; (1997)) for solving inverse Sturm-Liouville problems with a recent result by Kravchenko (Complex Variables and Elliptic Equations 2008; 53(8):775-789) giving accurate solutions of direct problems. Our construction allows one to recover the potential in situations of great importance in studying nanostructures including quantum dots when only a very limited number of eigenvalues (3-4) obtained experimentally is available.

AB - A method for reconstructing symmetric potentials of Schrödinger operators from a finite set of eigenvalues is presented. The method combines the approach developed by Rundell and Coworkers (SIAM Monographs on Mathematical Modeling and Computation. SIAM: Philadelphia, PA; (1997)) for solving inverse Sturm-Liouville problems with a recent result by Kravchenko (Complex Variables and Elliptic Equations 2008; 53(8):775-789) giving accurate solutions of direct problems. Our construction allows one to recover the potential in situations of great importance in studying nanostructures including quantum dots when only a very limited number of eigenvalues (3-4) obtained experimentally is available.

KW - Inverse problem

KW - Quantum dot

KW - Schrödinger equation

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U2 - 10.1002/mma.1218

DO - 10.1002/mma.1218

M3 - Artículo

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SP - 469

EP - 472

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 4

ER -

Reconstruction of potentials in quantum dots and other small symmetric structures

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Keywords

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