Quantization in curvilinear coordinates and construction of expansion formulas via eigenfunctions of Schrodinger operator
Alexander G. Chircov, Georgy A. Kazakov
In the present work the classical problem about a particle in a central field is quantized using Chirkov's method. According to this method, in contrast to classical one, quantization is carried out directly in spatial spherical coordinates. The generalization of Schrodinger equation for a case of spatial spherical coordinates is obtained. The expansion formulas of arbitrary functions via the eigenfunctions of this equation are obtained on the basis of Titchmarsh's method. It is proved that the Parseval equality is fulfilled directly in curvilinear coordinates.
Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 5, 2004•0 citations