Continuum Mechanics and Thermodynamics

, Volume 31, Issue 3, pp 639–667 | Cite as

A new class of exact solutions of the Schrödinger equation

  • E. E. PerepelkinEmail author
  • B. I. Sadovnikov
  • N. G. Inozemtseva
  • A. A. Tarelkin
Original Article


The aim of this paper is to find the exact solutions of the Schrödinger equation. As is known, the Schrödinger equation can be reduced to the continuum equation. In this paper, using the nonlinear Legendre transform the equation of continuity is linearized. Particular solutions of such a linear equation are found in the paper, and an inverse Legendre transform is considered for them with subsequent construction of solutions of the Schrödinger equation. Examples of the classical and quantum systems are considered.


Exact solution Schrödinger equation Legendre transform Nonlinear partial differential equation 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • E. E. Perepelkin
    • 1
    Email author
  • B. I. Sadovnikov
    • 1
  • N. G. Inozemtseva
    • 2
  • A. A. Tarelkin
    • 1
  1. 1.Faculty of PhysicsLomonosov Moscow State UniversityMoscowRussia
  2. 2.Dubna State UniversityMoscow Region, MoscowRussia

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