A new class of exact solutions of the Schrödinger equation

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 equa...

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Bibliographic Details
Published inContinuum mechanics and thermodynamics Vol. 31; no. 3; pp. 639 - 667
Main Authors Perepelkin, E. E., Sadovnikov, B. I., Inozemtseva, N. G., Tarelkin, A. A.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2019
Springer
Springer Nature B.V
Subjects
Classical and Continuum Physics
Differential equations
Engineering Thermodynamics
Exact solutions
Heat and Mass Transfer
Inverse problems
Linear equations
Linearization
Mathematical analysis
Original Article
Partial differential equations
Physics
Physics and Astronomy
Probability distributions
Schrodinger equation
Structural Materials
Theoretical and Applied Mechanics
Velocity
Nonlinear partial differential equation
Schrödinger equation
Legendre transform
Exact solution
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Summary: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.
ISSN:0935-1175
1432-0959
DOI:10.1007/s00161-018-0716-9