Institute of Physics Ministry of Science and Education Republic of Azerbaijan

EXACT SOLUTION OF THE RELATIVISTIC FINITE-DIFFERENCE EQUATION FOR THE RING-SHAPED OSCILLATOR POTENTIAL

¹Sh.M. Nagiyev, ²G.G. Quliyeva, ^1,2V.A. Tarverdiyeva

ABSTRACT

We solve exactly the relativistic finite-difference equation for the quantum three-dimensional ring-shaped oscillator potential. Our investigation is based on a finite-difference version of relativistic quantum mechanics. So-called relativistic configurational r-space is a key concept here. We show that the radial wavefunctions and angular wavefunctions are expressed through the continuous dual Hahn polynomials and Jacobi polynomials, respectively. A discrete energy spectrum has been found. The radial wave functions and energy spectrum have the correct nonrelativistic limit.

Keywords: Relativistic finite-difference equation of motion; ring oscillator potential; continuous dual Hahn and Jacobi polynomials; non-relativistic limit.
DOI:10.70784/azip.2.2025244

Received: 26.05.2025
Internet publishing: 30.05.2025 AJP Fizika A 2025 02 az p.44-50

AUTHORS & AFFILIATIONS

1. Institute of Physics Ministry of Science and Education Republic of Azerbaijan, 131 H.Javid ave. Baku, AZ 1073, Azerbaijan
2. Sumgayit State University of the Ministry of Science and Education, Sumgait, Azerbaijan, AZ 5008, 43rd m., Baki street, 1
E-mail: shakir.m.nagiyev@gmail.com, gulnara.quliyeva@sdu.edu.az, vefa.tarverdiyeva@sdu.edu.az

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