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Galilean Covariance and the Schrödinger Equation
Author(s) -
Omote M.,
Kamefuchi S.,
Takahashi Y.,
Ohnuki Y.
Publication year - 1989
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190371203
Subject(s) - galilean , wave function , covariance , general covariance , relativistic quantum mechanics , classical mechanics , physics , schrödinger equation , mathematical physics , basis (linear algebra) , relativistic quantum chemistry , quantum mechanics , mathematics , quantum , theoretical physics , quantum dynamics , general relativity , geometry , statistics
Galilei transformations are formulated in a 5‐dimensional form and on such basis the non‐relativistic quantum mechanics is reconstructed. Our approach has the following advantages over others'. (1) The Schrödinger wavefunctions are taken to be vector (not projective) representations of the Galilei group, so that (2) the problem here is considerably simplified. (3) The formulation proceeds in a way quite parallel to that of relativistic quantum mechanics, and what is most important, (4) Galilei covariance is manifest throughout.