Eigenvalues of the generalized helicity operator for spin 3/2 particle in the presence of the magnetic field and the projective operators method
https://doi.org/10.29235/1561-2430-2025-61-4-307-319
Abstract
The eigenvalue problem for generalized helicity operator for a spin 3/2 particle in presence of the uniform magnetic field is solved. After separating the variables in the basis of cylindrical coordinates (r, ϕ, z) and the tetrad, the system of 16 first-order differential equations in the variable r is derived. This system is studied with the use of the method of projective operators, constructed with the use of the third projection of the spin for the particle. In accordance with thе method by Fedorov – Gronskiy, all 16 variables may be expressed in terms of only 4 distinguished functions, which are constructed in terms of confluent hypergeometric functions. Further the problem reduces to studying the linear algebraic homogeneous system for 16 algebraic variables. In the end, we derive algebraic equations of the second and the fourth order, their roots determine the possible eigenvalues of the helicity operator.
About the Authors
A. V. Ivashkevich
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Belarus
Belarus
Alina V. Ivashkevich – Researcher
68-2, Nezavisimosti Ave., 220072, Minsk
V. V. Red’kov
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Belarus
Belarus
Viktor V. Red’kov – Dr. Sc. (Physics and Mathematics), Professor, Chief Researcher of the Center for Fundamental Interactions and Astrophysics
68-2, Nezavisimosti Ave., 220072, Minsk
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