Spherical solutions of the wave equation for a spin 3/2 particle
https://doi.org/10.29235/1561-8323-2019-63-3-282-290
Abstract
The wave equation for a spin 3/2 particle, described by 16-component vector-bispinor, is investigated in spherical coordinates. In the frame of the Pauli–Fierz approach, the complete equation is split into the main equation and two additional constraints, algebraic and differential. The solutions are constructed, on which 4 operators are diagonalized: energy, square and third projection of the total angular momentum, and spatial reflection, these correspond to quantum numbers {ε, j, m, P}. After separating the variables, we have derived the radial system of 8 first-order equations and 4 additional constraints. Solutions of the radial equations are constructed as linear combinations of the Bessel functions. With the use of the known properties of the Bessel functions, the system of differential equations is transformed to the form of purely algebraic equations with respect to three quantities a1, a2, a3. Its solutions may be chosen in various ways by solving the simple linear equation A1a1 + A2a2 + A3a3 = 0 where the coefficients Ai are expressed trough the quantum numbers ε, j. Two most simple and symmetric solutions have been chosen. Thus, at fixed quantum numbers {ε, j, m, P} there exists double-degeneration of the quantum states.
About the Authors
A. V. Ivashkevich
Mozyr State Pedagogical University named after I. P. Shamyakin
Belarus
Belarus
Ivashkevich Alina Valentinovna – Student
28, Studencheskaya Str., 247760, Mozyr, Gomel region, Republic of Belarus
E. M. Ovsiyuk
Mozyr State Pedagogical University named after I. P. Shamyakin
Belarus
Belarus
Оvsiyuk Еlena Мikhailovna – Ph. D. (Physics and Mathematics), Assistant professor
28, Studencheskaya Str., 247760, Mozyr, Gomel region, Republic of Belarus
V. V. Kisel
Belarusian State University of Informatics and Radioelectronics
Belarus
Belarus
Kisel Vasily Vasilyevich – Ph. D. (Physics and Mathematics), Assistant professor
6, P. Brovka Str., 220013, Minsk, Republic of Belarus
V. M. Red’kov
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Belarus
Belarus
Red’kov Viktor Mikhailovich – Ph. D. (Physics and Mathematics), Chief researcher
68-2, Nezavisimosti Ave., 220072, Minsk, Republic of Belarus
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