Group analysis of two-dimensional Schrödinger equations with variable mass

TitleGroup analysis of two-dimensional Schrödinger equations with variable mass
Publication TypeJournal Article
Year of Publication2015
AuthorsZasadko, TM
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2015.05.007
Issue5
SectionMathematics
Pagination7-14
Date Published5/2015
LanguageUkrainian
Abstract

The first-order integrals of motion for Schrödinger equations with variable mass are classified. Eight classes of such equations with non-equivalent symmetries are specified. They include integrable, superintegrable, and maximally superintegrable systems. A complete set of solutions for one of these systems is presented explicitly.
KeywordsHamiltonians, integrals of motion, integrated systems, Lie algebra, maximally superintegrable systems, Schrödinger equation, superintegrable systems
References: 
  1. Miller Jr.W., Post S., Winternitz P. J. Phys. A: Math. Theor., 2013, 46: 423001. https://doi.org/10.1088/1751-8113/46/42/423001
  2. Nikitin A.G., Zasadko T.N. Zbirnyk prats' Institutu Matematyky NAN Ukrainy, 2014, 11: 228–240 (in Ukrainian).
  3. Nikitin A.G., Zasadko T.N. J. Math. Phys., 2015, 56: 042101. https://doi.org/10.1063/1.4908107
  4. Nikitin A.G. J. Phys. A: Math. Theor., 2012, 45: 485204. https://doi.org/10.1088/1751-8113/45/48/485204
  5. Nikitin A.G. Ukr. Math. J., 1991, 43: 734–743. https://doi.org/10.1007/BF01058941
  6. Zhelubenko D.P., Shtern A. I. Representation of Lie groups, Moscow: Nauka, 1983 (in Russian).
  7. Fushchich V. I., Barannik L.F., Barannik A. F. Subgroup analysis of Galilei and Poincaré groups and reduction of nonlinear equations, Kyiv: Naukova Dumka, 1991 (in Russian).