Algebraic Solution of Gaunt Coefficients via the Angular Momentum Ladder Operators

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Sinop Üniversitesi Fen Bilimleri Dergisi
Volume:8 Issue:2
Algebraic Solution of Gaunt Coefficients via the Angular Momentum Ladder Operators

Algebraic Solution of Gaunt Coefficients via the Angular Momentum Ladder Operators

Pages : 229-244

View : 48 | Download : 53

Publication Date : 2023-12-28

Article Type : Research Paper

Abstract :In this study, Gaunt coefficients, frequently encountered in quantum mechanical calculations of atomic and molecular structures, have been algebraically derived. Firstly, the Gaunt coefficient, equal to the integral over the solid angle of the product of three spherical harmonics, is written in terms of angular momentum ladder operators. Subsequently, raising or lowering operators are applied to spherical harmonics, and the obtained integrals are solved using the recurrence and orthogonality relations of spherical harmonics. As a result, algebraic expressions for Gaunt coefficients are obtained in terms of quantum numbers.
Keywords : Gaunt katsayıları, merdiven işlemcileri, küresel harmonikler

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