Pure and Applied Mathematics Journal

| Peer-Reviewed |

Derivation of Schrödinger Equation from a Variational Principle

Received: 29 March 2013    Accepted:     Published: 30 August 2013
Views:       Downloads:

Share This Article

Abstract

The aim of this research is to derive Schrödinger equation from calculus of variations (variational principle), so we use the methodology of calculus of variations. The variational principle one of great scientific significance as they provide a unified approach to various mathematical and physical problems and yield fundamental exploratory ideas.

DOI 10.11648/j.pamj.20130204.12
Published in Pure and Applied Mathematics Journal (Volume 2, Issue 4, August 2013)
Page(s) 146-148
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Schrödinger Equation, Variatinal Principle, Hamiltonian-Jacobi Equation

References
[1] Abraham Albert Ungar –Analytic Hyperbolic Geometry and Albert Einstein's Special Theory Relativity-World Scientific publishing Co-Pte.Ltd, (2008).
[2] Al Fred Grany, Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press (1998).
[3] Aubin Thierry, Differential Geometry-American Mathematical Society (2001).
[4] Aurel Bejancu &Hani Reda Faran-Foliations and Geometric Structures, Springer Adordrecht, the Netherlands (2006).
[5] Bluman G.W & Kumei. S, Symmetry and Differential Equations New York: Springer-Verlag (1998).
[6] David Bleaker-Gauge Theory and Variational Principle, Addison- Wesley Publishing Company, (1981).
[7] Differential Geometry and the calculus of Variations, Report Hermann-New York and London, (1968).
[8] Edmund Bertschinger-Introduction to Tenser Calculus for General Relativity, (2002).
[9] M. Lee. John-Introduction to Smooth Manifolds-Springer Verlag, (2002).
[10] Elsgolts,L., Differential Equations and Calculus of variations, Mir Publishers,Moscow,1973.
[11] Lyusternik,L,A., The shortest Lines:Varitional Problems, Mir Publishers,Moscow,1976.
[12] Courant, R. and Hilbert,D. ,Methods of Mathematical Physics,Vols.1 and 2,Wiley – Interscince, New York,1953.
[13] Hardy,G.,Littlewood,J.E.and Polya,G.,Inqualities,(Paperback edition),Cambrige University Press,London,1988.
[14] Tonti,E.,Int. J. Engineering Sci.,22,P.1343,1984.
[15] Vladimirov,V.S.,A Collection of problems of the Equations of Mathematical Physics, Mir Publishers,Moscow,1986.
[16] Komkov,V.,Variational Principles of Continuum Mechanics with Engineering Applications,Vol.1,D.Reidel Publishing Co.,Dordecht,Holland,1985.
[17] Nirenberg,L.,Topic in Calculus of Variations (edited by M.Giaquinta),P.100,Springer – Verlag,Berlin 1989.
Author Information
  • Umm Al-qura University –KSA-University College of Al- Qunfudah, Zip code 21912 – box 1109

Cite This Article
  • APA Style

    Sami. H. Altoum. (2013). Derivation of Schrödinger Equation from a Variational Principle. Pure and Applied Mathematics Journal, 2(4), 146-148. https://doi.org/10.11648/j.pamj.20130204.12

    Copy | Download

    ACS Style

    Sami. H. Altoum. Derivation of Schrödinger Equation from a Variational Principle. Pure Appl. Math. J. 2013, 2(4), 146-148. doi: 10.11648/j.pamj.20130204.12

    Copy | Download

    AMA Style

    Sami. H. Altoum. Derivation of Schrödinger Equation from a Variational Principle. Pure Appl Math J. 2013;2(4):146-148. doi: 10.11648/j.pamj.20130204.12

    Copy | Download

  • @article{10.11648/j.pamj.20130204.12,
      author = {Sami. H. Altoum},
      title = {Derivation of Schrödinger Equation from a Variational Principle},
      journal = {Pure and Applied Mathematics Journal},
      volume = {2},
      number = {4},
      pages = {146-148},
      doi = {10.11648/j.pamj.20130204.12},
      url = {https://doi.org/10.11648/j.pamj.20130204.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.20130204.12},
      abstract = {The aim of this research is to derive Schrödinger equation from calculus of variations (variational principle), so we use the methodology of calculus of variations. The variational principle one of great scientific significance as they provide a unified approach to various mathematical and physical problems and yield fundamental exploratory ideas.},
     year = {2013}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Derivation of Schrödinger Equation from a Variational Principle
    AU  - Sami. H. Altoum
    Y1  - 2013/08/30
    PY  - 2013
    N1  - https://doi.org/10.11648/j.pamj.20130204.12
    DO  - 10.11648/j.pamj.20130204.12
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
    SP  - 146
    EP  - 148
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.20130204.12
    AB  - The aim of this research is to derive Schrödinger equation from calculus of variations (variational principle), so we use the methodology of calculus of variations. The variational principle one of great scientific significance as they provide a unified approach to various mathematical and physical problems and yield fundamental exploratory ideas.
    VL  - 2
    IS  - 4
    ER  - 

    Copy | Download

  • Sections