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.
Date Published5/2015

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
  1. Miller Jr.W., Post S., Winternitz P. J. Phys. A: Math. Theor., 2013, 46: 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.
  4. Nikitin A.G. J. Phys. A: Math. Theor., 2012, 45: 485204.
  5. Nikitin A.G. Ukr. Math. J., 1991, 43: 734–743.
  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).