Spin 1 Particle With Anomalous Magnetic Moment in External Uniform Electric Field, Solutions With Cylindrical Symmetry

ABSTRACT A generalized 10‐dimensional Duffin–Kemmer–Petiau equation for spin 1 particle with anomalous magnetic moment is examined in cylindrical coordinates (t,r,ϕ,z)$$ \left(t,r,\phi, z\right) $$ in the presence of the external uniform electric field oriented along the axis z$$ z $$. On solutions,...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 48; no. 9; pp. 9640 - 9652
Main Authors: Ivashkevich, Alina, Red'kov, Viktor, Chichurin, Alexander
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 01.06.2025
Subjects:
Angular momentum
anomalous magnetic moment
Bessel functions
Cylindrical coordinates
cylindrical symmetry
Differential equations
Electric fields
exact solutions
external electric field
Hypergeometric functions
Magnetic moments
method of the projective operators
Operators (mathematics)
partial differential equations
Particle spin
spin 1 particle
Symmetry
ISSN:0170-4214, 1099-1476
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Summary:ABSTRACT A generalized 10‐dimensional Duffin–Kemmer–Petiau equation for spin 1 particle with anomalous magnetic moment is examined in cylindrical coordinates (t,r,ϕ,z)$$ \left(t,r,\phi, z\right) $$ in the presence of the external uniform electric field oriented along the axis z$$ z $$. On solutions, we diagonalize operators of the energy and third projection of the total angular momentum. First, we derive the system of 10 equations in partial derivatives for functions Fi(r,z)=Gi(r)Hi(z)(i=1,10‾)$$ {F}_i\left(r,z\right)={G}_i(r){H}_i(z)\kern0.3em \left(i=\overline{1,10}\right) $$. The use of the method based on the projective operators permits us to express 10 variables Gi(r)$$ {G}_i(r) $$ through only three different functions f1(r),f2(r),f3(r)$$ {f}_1(r),{f}_2(r),{f}_3(r) $$, which are solved in Bessel functions. After that, we derive the system of 10 first‐order differential equations for functions Hi(z)$$ {H}_i(z) $$. This system reduces to one independent equation for a separate function and to the system of two linked equations for two remaining primary functions. This system after diagonalization of the mixing matrix gives two separated equations for new variables. All three equations for basic functions are solved in terms of the confluent hypergeometric functions. Thus, the complete system of solutions with cylindrical symmetry for the vector particle with anomalous magnetic moment in the presence of the external uniform electric field is found.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.10831