Quantization in curvilinear coordinates and construction of expansion formulas via eigenfunctions of Schrödinger operator

Alexander G. Chircov; George A. Kazakov

doi:10.1117/12.555368

5 April 2004 Quantization in curvilinear coordinates and construction of expansion formulas via eigenfunctions of Schrodinger operator

Alexander G. Chircov, George A. Kazakov

Author Affiliations +

Proceedings Volume 5400, Seventh International Workshop on Nondestructive Testing and Computer Simulations in Science and Engineering; (2004) https://doi.org/10.1117/12.555368
Event: 2003 Chapter books, 2003, Bellingham, WA, United States

Abstract

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.

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Alexander G. Chircov and George A. Kazakov "Quantization in curvilinear coordinates and construction of expansion formulas via eigenfunctions of Schrodinger operator", Proc. SPIE 5400, Seventh International Workshop on Nondestructive Testing and Computer Simulations in Science and Engineering, (5 April 2004); https://doi.org/10.1117/12.555368

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