Derivation of Schrödinger Equation from a Variational Principle

Sami. H. Altoum

doi:doi:10.11648/j.pamj.20130204.12

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Derivation of Schrödinger Equation from a Variational Principle

Sami. H. Altoum

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 4)

Received: 29 March 2013 Published: 30 August 2013

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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.

Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 4)
DOI	10.11648/j.pamj.20130204.12
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), 2013. Published by Science Publishing Group

Keywords

Schrödinger Equation, Variatinal Principle, Hamiltonian-Jacobi Equation

References

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[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.
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[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.

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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

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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

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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

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@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://article.sciencepublishinggroup.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}
}

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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
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VL  - 2
IS  - 4
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Author Information

Sami. H. Altoum

Umm Al-qura University –KSA-University College of Al- Qunfudah, Zip code 21912 – box 1109

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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

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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

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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://article.sciencepublishinggroup.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