EXACT WAVE FUNCTIONS AND DYNAMICAL SYMMETRY GROUP FOR THE MODIFIED NONRELATIVISTIC RING-SHAPED KRATZER POTENTIAL
Shakir M. Nagiyev, Könül Sh. Jafarova, Shovqiyya A. Amirova, Vefa A. Tarverdiyeva,
2024   03   en   p.03-08

ABSTRACT

We propose a new exactly solvable potential which consists of the modified Kratzer potential plus a new ring-shaped potential ((β+γcosθ+νcos2 θ))/(r2sin2θ). The exact solutions of the bound states of the Schrödinger equation for this potential are presented analytically by using the functional method. The wavefunctions of the radial and angular parts are taken on the form of the Laguerre polynomials and the Jacobi polynomials, respectivly. Total energy of the system is different from the modified Kratzer potential because of the contribution of the angular part. We also build a dynamical symmetry group for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically.

Keywords: Schrödinger equation; ring-shaped modified Kratzer potential; dynamical symmetry group; Laguerre and Jacobi polynomials.
DOI:10.70784/azip.1.2024303

Received: 08.07.2024
Internet publishing: 14.08.2024

AUTHORS & AFFILIATIONS

Institute of Physics Ministry of Science and Education Republic of Azerbaijan, 131 H.Javid ave, Baku, AZ-1143, Azerbaijan
E-mail: shakir.m.nagiyev@gmail.com, konule2016@gmail.com, shovqiyya@mail.ru, vefa.tarverdiyeva@mail.ru

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