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AIP conference proceedings

Non-relativistic energy analysis of the pauli equation for the Pöschl-teller potential under the influence of the Aharonov-Bohm flux

Muhammad Adi Kusuma, Suci Faniandari, Jeriko Panjaitan, Rendi Oktafian Ali Saputra, Loveando Mozart Marchiell Notosuroto

Published Jan 1, 2026• 0 citations
Publisher

Abstract

The hyperbolic Pöschl-Teller provides an analytically tractable model for studying bound states and represents an exactly solvable quantum system. However, the solvability of this system under the influence of an Aharonov-Bohm (AB) flux, and particularly for spin particles governed by the Pauli equation, remains largely unexplored within this framework. The present study bridges this gap by formulating and solving the Pauli equation for spin particles in cylindrical coordinates by applying a hyperbolic Pöschl-Teller potential with an Aharonov-Bohm flux field. Using the Hypergeometric method and variable separation, we derive the explicit quantization conditions that determine the energy spectrum. Key findings reveal spin-dependent energy shifts due to the interaction between the particle’s intrinsic magnetic moment and the AB flux field. Our work not only expands the study of analytically solvable quantum models but also highlights the intrinsic particle behavior arising from spin-field interactions in non-trivial geometries.

DOI
10.1063/12.0044728

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The hyperbolic Pöschl-Teller provides an analytically tractable model for studying bound states and represents an exactly solvable quantum system. However, the solvability of this system under the influence of an Aharonov-Bohm (AB) flux, and particularly for spin particles governed by the Pauli equation, remains largely unexplored within this framework. The present study bridges this gap by formulating and solving the Pauli equation for spin particles in cylindrical coordinates by applying a hyperbolic Pöschl-Teller potential with an Aharonov-Bohm flux field. Using the Hypergeometric method and variable separation, we derive the explicit quantization conditions that determine the energy spectrum. Key findings reveal spin-dependent energy shifts due to the interaction between the particle’s intrinsic magnetic moment and the AB flux field. Our work not only expands the study of analytically solvable quantum models but also highlights the intrinsic particle behavior arising from spin-field interactions in non-trivial geometries.
An approximate solution of the Dirac equation for a spin-1/2 particle under the influence of q -deformed hyperbolic Pöschl–Teller potential combined with trigonometric Scarf II non-central potential is studied analytically. It is assumed that the scalar potential equals the vector potential in order to obtain analytical solutions. Both radial and angular parts of the Dirac equation are solved using the Nikiforov–Uvarov method. A relativistic energy spectrum and the relation between quantum numbers can be obtained using this method. Several quantum wave functions corresponding to several states are also presented in terms of the Jacobi Polynomials.
Abstract In this work, the position-dependent mass Schrödinger equation is solved with the Pöschl-Teller-like potential in the presence of magnetic and Aharonov–Bohm (AB) flux fields. The BenDaniel-Duke ambiguity parameter ordering is used to formulate the Hamiltonian operator for the system. An approximate analytical equation of the bound-state energy spectrum is obtained using the parametric Nikiforov-Uvarov solution technique along with a Pekeris-like approximation scheme. With the aid of the obtained equation for the energy levels, analytical formulas of magnetization and magnetic susceptibility at zero-temperature are derived and subsequently used to predict the physical properties of diatomic substances including the ground state H 2 , HCl, CO and LiH molecules. The expression for the bound-state-energy spectrum is used to generate numerical data for the molecules. The computed energy eigenvalues agree with the literature on diatomic molecules. The study revealed that in the absence of the external fields, the energy eigenvalues and magnetic susceptibility of the system are degenerate. However, with only a low intensity AB field, the degeneracy is completely eliminated from the energy states of the molecules.
The 2D Pauli equation with Hulthén potential for spin-1/2 particle in the presence of Aharonov—Bohm (AB) field is solved analytically, on the assumption that an effective approximation is used for the centrifugal term. Singular and regular solutions of the problem are obtained. It is shown that the AB field lifts the degeneracy of the energy levels. The range of the flux parameter for which singular solutions are allowed is modified compared to the pure AB case. When the screening parameter vanishes, it is shown that the obtained energy spectrum becomes the same as that of the Aharonov—Bohm Coulomb problem.
Invariant operator method for discrete or continuous spectrum eigenvalue and unitary transformation approach are employed to study the two-dimensional time-dependent Pauli equation in presence of the Aharonov–Bohm effect (AB) and external scalar potential. For the spin particles the problem with the magnetic field is that it introduces a singularity into wave equation at the origin. A physical motivation is to replace the zero radius flux tube by one of radius R, with the additional condition that the magnetic field be confined to the surface of the tube, and then taking the limit R → 0 at the end of the computations. We point that the invariant operator must contain the step function θ(r – R). Consequently, the problem becomes more complicated. In order to avoid this difficulty, we replace the radius R by ρ(t)R, where ρ(t) is a positive time-dependent function. Then at the end of calculations we take the limit R → 0. The qualitative properties for the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation satisfied by ρ(t), i.e., C > 0, C = 0, and C < 0. Following the C's values the spectrum of quantum states is discrete (C > 0) or continuous (C ≤ 0).
In this present work, we study the approximate solution of the Schrodinger equation with hyperbolic function position-dependent mass for a symmetrical Modified Poschl-Teller potential. We consider the system influenced by the external hyperbolic magnetic and Aharonov-Bohm (AB) forces. By using the Laplace transform method, the second-order differential equation of the Schrodinger equation is reduced to a first-order differential equation and so the eigenfunction and energy eigenvalues are obtained. The behavior of the bound state energy levels was demonstrated and analyzed using the computational method for various values of the potential parameter, mass parameter, external magnetic force, and AB force. Moreover, the thermomagnetic properties of the system were analyzed for H2, LiH, and HCl diatomic particles, involving the vibrational mean energy, vibrational free energy, vibrational entropy, specific heat capacity, magnetization, magnetic susceptibility, and persistent current.
We investigate the scattering of a charged quantum particle in a helically twisted background that induces an effective Coulomb-like interaction, in the presence of an Aharonov-Bohm (AB) flux. Starting from the nonrelativistic Schrödinger equation in the twisted metric, we derive the radial equation and show that, after including the AB potential, it can be mapped onto the same Kummer-type differential equation that governs the planar 2D2D2D Coulomb +++ AB problem, with a geometry-induced Coulomb strength and the azimuthal quantum number shifted as m→m−λm\to m-λm→m−λ. We construct the exact scattering solutions, obtain closed expressions for the partial-wave SSS matrix and phase shifts, and derive the corresponding scattering amplitude, differential cross section, and total cross section. We also show that the pole structure of the SSS matrix is consistent with the bound-state quantization previously obtained for the helically twisted Coulomb-like problem.