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On Hamiltonian Formulations of the Schrödinger System

✍ Scribed by László Á. Gergely

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
86 KB
Volume
298
Category
Article
ISSN
0003-4916

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✦ Synopsis

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.

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