The quantum characteristics of a class of complicated double ring-shaped non-central potential

Abstract

Firstly we outline how to obtain the normalized polar angular wave functions of the Schrödinger equation with a class of complicated double ring-shaped non-central potential by introducing the super-universal associated Legendre polynomials, and present the exact energy equation and normalized radial wave functions for the given central potentials, such as the harmonic oscillator and Coulomb potential. We then discuss in detail the quantum characteristics of the polar and radial wave functions and energy equation, and their reducing problems. These features include bound state relations between the harmonic oscillator and Coulomb potential quantum systems, and degeneracy of their energy levels. We also observe that the bound state relations, including the energy levels and wave functions for the harmonic oscillator and Coulomb potential systems, can be obtained from each other by mapping the system parameters. Special cases related to reduction questions are discussed in detail.

Analysis of Energy and Wave Functions and the Thermodynamics Properties of the 6-Dimensional Schrodinger Equation Under Double Ring-Shape Oscillator (Drso) and Manning-Rosen Potentials Using Susy Qm Method

“…This potential type in recent times has been an interesting topic of researchers in physics and quantum chemistry because of its importance when applied to describe the structure of benzene molecules in quantum chemistry and deformed nuclei in nuclear physics. Ring-shaped harmonic oscillators are also used to study the spin symmetry of an antinucleon embedded in nucleus and the linear and nonlinear optical effects of moving electrons in the non-central field (Chang-Yuan, et al, 2013; Fa-Lin, Lu and Chang-Yuan, 2010; Hassanabadi, et al, 2014;Ikot, A. N., et al, 2016;Sun, et al, 2014;Yasuk and Durmus, 2007;You et al, 2018).…”

Solutions of the D-Dimensional Schrödinger Equation with the Hyperbolic Pöschl-Teller Potential plus Modified Ring-Shaped Term

“…Motivated by the recent studies of the ring-shaped potential [29][30][31][32], we proposed a novel hyperbolical Pöschl-Teller potential plus generalized ring-shaped potential of the form (see Figure 1) where is the screening parameter and , , , , and are real potential parameters. As a special case when → 0 with…”

“…Cheng and Dai investigated modified Kratzer potential plus the new ring shaped potential using Nikiforov-Uvarov method [14]. Recently, Ikot et al [15][16][17] investigated the Schrödinger equation with Hulthen plus a new ring shape potential [13],Non-spherical harmonic and Coulomb potential [16] and pseudo-Coulomb potential in the cosmic string space-time [17].Many authors have used different methods to obtain exact solutions of the wave equation such as the methods of Supersymmetric Quantum Mechanics (SUSY-QM) [18][19][20], the Tridiagonal Representation Approach (TRA) [21][22][23][24], Nikiforov-Uvarov (NU) [25][26][27][28][29] among other methods Motivated by the recent studies of the ring shaped-like potential [30][31][32][33], we proposed a novel hyperbolical Poschl Teller potential plus generalized ring shaped potential of the form,…”

The Visualization of the Space Probability Distribution for a Particle Moving in a Double Ring-Shaped Coulomb Potential

“…[7,8,13,14,26]. Among them the SPDs have been carried out, but their studies are either treated for the radial part in spherical shell ( , ) r r dr + or for the angular parts [27,28]. The discussions mentioned above are only concerned with one or two of three variables ( ) , , r θ ϕ .…”