On singular Lagrangian underlying the Schrödinger equation

A. A. Deriglazov

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 = (- frac(ℏ2, 2 m) Δ + V) φ{symbol} + i ℏ ∂t φ{symbol}, where the real field φ{symbol} (t, xi) is some solution of nonsingular Lagrangian theory being specified below. Preservation of probability turns out to be the energy conservation law for the field φ{symbol}. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics.

Original languageEnglish
Pages (from-to)3920-3923
Number of pages4
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume373
Issue number43
DOIs
Publication statusPublished - 19 Oct 2009

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Keywords

  • Constrained theories
  • Lagrangian formulation
  • Schrödinger equation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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