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The method of zero range potential (ZRP) for one-electron problems isreviewed. In the absence of an external electromagnetic field, the notion of aZRP is introduced from different points of view and for an arbitrary dimensionof space. Then, three-dimensional problems of motion of an electron in thefield of several ZRPs and laser radiation are studied. Exact wave functions forthe processes of photoionization and stimulated bremsstrahlung in the presenceof the laser field of an arbitrary pulse shape are obtained in the form ofone-dimensional integral representations.

An electron in the presence of multiple zero range potentials and an  external laser field -- exact solutions for photoionization and stimulated  bremsstrahlung