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Journal of Mathematical Physics / Volume 52 / Issue 4 / ARTICLES / Methods of Mathematical Physics

J. Math. Phys. 52, 043522 (2011); http://dx.doi.org/10.1063/1.3579991 (10 pages)

Dispersion equation and eigenvalues for quantum wells using spectral parameter power series

Raúl Castillo-Pérez1, Vladislav V. Kravchenko2, Héctor Oviedo-Galdeano1, and Vladimir S. Rabinovich1

1SEPI, ESIME, National Polytechnic Institute, Av. IPN S/N, C.P. 07738, Mexico City, México
2Department of Mathematics, CINVESTAV del IPN, Campus Querétaro, Apartado Postal 1-798, Arteaga # 5, Col. Centro, Santiago de Querétaro, Qro., 76001 México

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(Received 7 December 2010; accepted 28 March 2011; published online 27 April 2011)

We derive a dispersion equation for determining eigenvalues of inhomogeneous quantum wells in terms of spectral parameter power series and apply it for the numerical treatment of eigenvalue problems. The method is algorithmically simple and can be easily implemented using available routines of such environments for scientific computing as MATLAB.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. SOLUTION IN THE INHOMOGENEOUS LAYER
  3. DERIVATION OF THE DISPERSION EQUATION
  4. NUMERICAL IMPLEMENTATION AND EXAMPLES
    1. The square-well potential
    2. The sech-squared potential
    3. The truncated quartic oscillator
    4. Asymmetric quantum well
    5. Potential from Fig.
  5. CONCLUSIONS

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KEYWORDS and PACS

Keywords

eigenvalues and eigenfunctions, quantum wells, Schrodinger equation

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3579991

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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