On Hamiltonian formulations of the Schrödinger system

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7 Citations (Scopus)

Abstract

We review and compare different variational formulations for the Schrödinger field. Some of them rely on the addition of a conveniently chosen total time derivative to the hermitic Lagrangian. Alternatively, the Dirac-Bergmann algorithm yields the Schrödinger equation first as a consistency condition in the full phase space, second as canonical equation in the reduced phase space. The two methods lead to the same (reduced) Hamiltonian. As a third possibility, the Faddeev-Jackiw method is shown to be a shortcut of the Dirac method. By implementing the quantization scheme for systems with second class constraints, inconsistencies of previous treatments are eliminated.

Original languageEnglish
Pages (from-to)394-402
Number of pages9
JournalAnnals of Physics
Volume298
Issue number2
DOIs
Publication statusPublished - Jun 15 2002

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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