Optimization of kinetic energy of a micro-object by impulse fields

The generalization is performed of the Schrodinger equation for the kinetic energy of a micro-object to potential fields with the structure of distribution of the first order of singularity. This made it possible to solve the problem of minimization of the kinetic energy of a micro-object at the prescribed level of its observation in the class of potentials concentrated in a limited volume with a smooth surface. It was found that the singular component of the optimal potential is a simple layer concentrated at the volume boundary. Graphs are displayed of some affine transformations of the squares of optimal wave functions and appropriate potentials.