Nonrelativistic particles in the presence of a Cariñena–Perelomov–Rañada–Santander oscillator and a disclination

2020 ◽  
Vol 35 (17) ◽  
pp. 2050071 ◽  
Author(s):  
Soroush Zare ◽  
Hassan Hassanabadi ◽  
Marc de Montigny
Keyword(s):  
Schrödinger Equation ◽  
Elastic Medium ◽  
Schrodinger Equation ◽  
Nonlinear Oscillator ◽  
Wave Functions ◽  
Oscillator Potential ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation ◽  
Exactly Solvable ◽  
Heun Functions

We examine an elastic medium with a disclination and consider the topological effects in the presence of a nonpolynomial quantum exactly solvable nonlinear oscillator potential related to the isotonic oscillator, and to which we refer as the Cariñena–Perelomov–Rañada–Santander (CPRS) potential. We obtain the wave functions, which are related to the confluent Heun functions, as well as the energy eigenvalues by solving exactly the corresponding radial Schrödinger equation.

scholarly journals The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

2016 ◽  
Vol 25 (01) ◽  
pp. 1650002 ◽  
Author(s):  
V. H. Badalov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Wave Functions ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Pekeris Approximation

In this work, the analytical solutions of the [Formula: see text]-dimensional radial Schrödinger equation are studied in great detail for the Wood–Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov–Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential [Formula: see text], the radial [Formula: see text] and orbital [Formula: see text] quantum numbers and parameters [Formula: see text] are defined as well.

scholarly journals Multidimensional Schrödinger Equation and Spectral Properties of Heavy-Quarkonium Mesons at Finite Temperature

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
M. Abu-Shady
Keyword(s):  
Schrödinger Equation ◽  
Quark Gluon Plasma ◽  
Plasma Diagnostics ◽  
Finite Temperature ◽  
Schrodinger Equation ◽  
Gluon Plasma ◽  
Wave Functions ◽  
Heavy Quarkonium ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation

TheN-radial Schrödinger equation is analytically solved at finite temperature. The analytic exact iteration method (AEIM) is employed to obtain the energy eigenvalues and wave functions for all statesnandl. The application of present results to the calculation of charmonium and bottomonium masses at finite temperature is also presented. The behavior of the charmonium and bottomonium masses is in qualitative agreement with other theoretical methods. We conclude that the solution of the Schrödinger equation plays an important role at finite temperature that the analysis of the quarkonium states gives a key input to quark-gluon plasma diagnostics.

scholarly journals Q-Deformed Morse and Oscillator Potential

2017 ◽  
Vol 2017 ◽  
pp. 1-4 ◽  
Author(s):  
H. Hassanabadi ◽  
W. S. Chung ◽  
S. Zare ◽  
S. B. Bhardwaj
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Analytic Solutions ◽  
Wave Functions ◽  
Oscillator Potential ◽  
Energy Eigenvalues

We studied the q-deformed Morse and harmonic oscillator systems with appropriate canonical commutation algebra. The analytic solutions for eigenfunctions and energy eigenvalues are worked out using time-independent Schrödinger equation and it is also noted that these wave functions are sensitive to variation in the parameters involved.

EXACT WAVE FUNCTIONS AND ENERGIES OF A NON-RELATIVISTIC FREE QUANTUM PARTICLE ON THE SURFACE OF A DEGENERATE TORUS

2004 ◽  
Vol 19 (23) ◽  
pp. 1759-1766 ◽  
Author(s):  
AXEL SCHULZE-HALBERG
Keyword(s):  
Schrödinger Equation ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Quantum Particle ◽  
Azimuthal Angle ◽  
Polar Angle ◽  
Wave Functions ◽  
Exactly Solvable

We study the non-relativistic Schrödinger equation for a free quantum particle constrained to the surface of a degenerate torus, parametrized by its polar and azimuthal angle. On restricting to wave functions that depend on the polar angle only, the Schrödinger equation becomes exactly-solvable. We compute its physical solutions (continuous, normalizable and 2π-periodic) and the associated energies in closed form.

scholarly journals ANALYTICAL SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE WOODS–SAXON POTENTIAL FOR ARBITRARY l STATE

2009 ◽  
Vol 18 (03) ◽  
pp. 631-641 ◽  
Author(s):  
V. H. BADALOV ◽  
H. I. AHMADOV ◽  
A. I. AHMADOV
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Pekeris Approximation

In this work, the analytical solution of the radial Schrödinger equation for the Woods–Saxon potential is presented. In our calculations, we have applied the Nikiforov–Uvarov method by using the Pekeris approximation to the centrifugal potential for arbitrary l states. The bound state energy eigenvalues and corresponding eigenfunctions are obtained for various values of n and l quantum numbers.

Analytical bound-state solutions of the Schrödinger equation for the Manning–Rosen plus Hulthén potential within SUSY quantum mechanics

2018 ◽  
Vol 33 (03) ◽  
pp. 1850021 ◽  
Author(s):  
A. I. Ahmadov ◽  
Maria Naeem ◽  
M. V. Qocayeva ◽  
V. A. Tarverdiyeva
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Bound State ◽  
Wave Functions ◽  
Hulthén Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Hulthen Potential

In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning–Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any [Formula: see text] angular momentum case via the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.

scholarly journals Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential

2019 ◽  
Vol 34 (14) ◽  
pp. 1950107 ◽  
Author(s):  
V. H. Badalov ◽  
B. Baris ◽  
K. Uzun
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Basis Set ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions

The formal framework for quantum mechanics is an infinite number of dimensional space. Hereby, in any analytical calculation of the quantum system, the energy eigenvalues and corresponding wave functions can be represented easily in a finite-dimensional basis set. In this work, the approximate analytical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood–Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are derived for any angular momentum case by means of state-of-the-art Nikiforov–Uvarov and supersymmetric quantum mechanics methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transforming each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well [Formula: see text] and [Formula: see text], the radial [Formula: see text] and [Formula: see text] orbital quantum numbers and parameters [Formula: see text], [Formula: see text], [Formula: see text] are also identified in detail. Next, the bound state energies and corresponding normalized hyper-radial wave functions for the neutron system of the [Formula: see text]Fe nucleus are calculated in [Formula: see text] and [Formula: see text] as well as the energy spectrum expressions of other higher dimensions are revealed by using the energy spectrum of [Formula: see text] and [Formula: see text].

The bound state solutions of the D-dimensional Schrödinger equation for the Hulthén potential within SUSY quantum mechanics

2017 ◽  
Vol 26 (05) ◽  
pp. 1750028 ◽  
Author(s):  
H. I. Ahmadov ◽  
M. V. Qocayeva ◽  
N. Sh. Huseynova
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Energy Levels ◽  
Wave Functions ◽  
Hulthén Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Hulthen Potential

In this paper, the analytical solutions of the [Formula: see text]-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any [Formula: see text] orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary [Formula: see text] states for [Formula: see text]-dimensional space.

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