Distortion of a Phase Space Under the Darboux Transformation

The Darboux transformation operator technique is applied to construct exactly solvable anharmonic singular oscillator potentials and to study their coherent states. Classical system corresponding to a transformed quantum system is constructed with the help of the coherent states technique. It is shown that at classical level the Darboux transformation may be treated as a transformation of K\"ahler potential which leads to a distortion of the initial phase space.