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The Fokker-Planck equation associated with the two - dimensional stationarySchr\"odinger equation has the conservation low form that yields a pair ofpotential equations. The special form of Darboux transformation of thepotential equations system is considered. As the potential variable is anonlocal variable for the Schr\"odinger equation that provides the nonlocalDarboux transformation for the Schr\"odinger equation. This nonlocaltransformation is applied for obtaining of the exactly solvable two -dimensional stationary Schr\"odinger equations. The examples of exactlysolvable two - dimensional stationary Schr\"odinger operators with smoothpotentials decaying at infinity are obtained.

The exactly solvable two-dimensional stationary Schr\"odinger operators obtaining by the nonlocal Darboux transformation