On singular lagrangian underlying the Schrodinger equation

Alexei Deriglazov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We analyze the properties that manifest hamiltonian nature of the Schrödinger equation and show that it can be considered as originating from singular Lagrangian action (with two second class constraints presented in the Hamiltonian formulation). It is used to show that any solution of the Schrödinger equation with time independent potential can be presented in the form ψ = (-h 2/2mδ V)φ + ih̄eφ tf, where the real field φ(t, x i) is some solution of nonsingular Lagrangian theory being specified below. Preservation of probability turns out to be the energy conservation law for the field f. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics.

Original languageEnglish
Title of host publicationProceedings of Science
Publication statusPublished - 2009
Event5th International School on Field Theory and Gravitation, ISFTG 2009 - Cuiaba City, Brazil
Duration: 20 Apr 200924 Apr 2009

Other

Other5th International School on Field Theory and Gravitation, ISFTG 2009
CountryBrazil
CityCuiaba City
Period20.4.0924.4.09

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ASJC Scopus subject areas

  • General

Cite this

Deriglazov, A. (2009). On singular lagrangian underlying the Schrodinger equation. In Proceedings of Science