A new class of exact solutions of the Schrödinger equation

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 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 Schrodinger equation. Examples of the classical and quantum systems are considered.