Journal of Mathematical Physics, Analysis, Geometry
2018, vol. 14, No 4, pp. 519-531   https://doi.org/10.15407/mag14.04.519     ( to contents , go back )
https://doi.org/10.15407/mag14.04.519

The Maximal "Kinematical" Invariance Group for an Arbitrary Potential Revised

A.G. Nikitin

Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka Street, Kyiv-4, 01001, Ukraine
E-mail: nikitin@imath.kiev.ua

Received March 3, 2018.

Dedicated to Professor V.A. Marchenko on his 95th birthday

Abstract

Group classification of one particle Schrödinger equations with arbitrary potentials (C.P. Boyer, Helv. Phys. Acta 47 (1974), p. 450) is revised. The corrected completed list of non-equivalent potentials and the corresponding symmetries is presented together with exact identification of symmetry algebras and admissible equivalence transformations.

Mathematics Subject Classification 2000: 34L15, 34L20, 35R10.
Key words: Schrödinger equation, Lie symmetries, equivalence transformations.

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