  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.
