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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus / Röpke, Gerd / Steeb, Willi-Hans

12 Issues per year


IMPACT FACTOR 2016: 1.432

Cite Score 2016: 1.35

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Source Normalized Impact per Paper (SNIP) 2016: 0.594

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1865-7109
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Volume 56, Issue 8 (Aug 2001)

Issues

Energy Eigenvalue Level Motion with Two Parameters

Willi-Hans Steeb
  • Corresponding author
  • International School for Scientific Computing, Rand Afrikaans University, RO. Box 524, Auckland Park 2006, South Africa
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/ Yorick Hardy
  • International School for Scientific Computing, Rand Afrikaans University, RO. Box 524, Auckland Park 2006, South Africa
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/ Ruedi Stoop
  • International School for Scientific Computing, Rand Afrikaans University, RO. Box 524, Auckland Park 2006, South Africa
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Published Online: 2014-06-02 | DOI: https://doi.org/10.1515/zna-2001-0805

Abstract

From the eigenvalue equation Ĥλ|(ψn)〉 = En(λ)|ψn(λ)〉 where Ĥ0 = Ĥ0 + XV̂ one can derive an autonomous system of first order ordinary differential equations for the eigenvalues En(λ) and the matrix elements Vmn(λ) := 〈ψm|V̂|ψn(λ)〉 where λ is the independent variable. We derive the partial differential equations for the extended case Ĥλ1λ2= Ĥ0 + λ11 + X22, where λ1 and λ2 are the independent variables. Some applications of this system of partial differential equations are discussed.

Keywords: Eigenvalue Level Motion; Partial Differential Equations

About the article

Received: 2001-04-17

Published Online: 2014-06-02

Published in Print: 2001-08-01


Citation Information: Zeitschrift für Naturforschung A, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2001-0805.

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© 1946 – 2014: Verlag der Zeitschrift für Naturforschung. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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