A new class of exact solutions of the Schrodinger equation
E.E. Perepelkin, B.I. Sadovnikov, N.G. Inozemtseva, A.A. Tarelkin
TL;DR
This paper introduces a novel method using the non-linear Legendre transform to find exact solutions of the Schrödinger equation, providing a new analytical approach for classical and quantum systems.
Contribution
It presents a new technique employing the non-linear Legendre transform to linearize and solve the Schrödinger equation exactly, which is a novel analytical contribution.
Findings
Derived exact solutions for specific classical and quantum systems.
Demonstrated the effectiveness of the non-linear Legendre transform in solving the Schrödinger equation.
Provided examples illustrating the application of the method.
Abstract
The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear 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 Schrodinger equation. Examples of the classical and quantum systems are considered.
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