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.

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.

Solving of the Schrodinger equation analytically with an approximated scheme of the Woods–Saxon potential by the systematical method of Nikiforov–Uvarov

2020 ◽  
Vol 29 (06) ◽  
pp. 2050032
Author(s):  
Enayatolah Yazdankish
Keyword(s):  
Schrödinger Equation ◽  
Exponential Type ◽  
Schrodinger Equation ◽  
Analytic Solutions ◽  
Centrifugal Term ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Nu Method

The analytic solutions of the Schrodinger equation for the Woods–Saxon (WS) potential and also for the generalized WS potential are obtained for the [Formula: see text]-wave nonrelativistic spectrum, with an approximated form of the WS potential and centrifugal term. Due to this fact that the potential is an exponential type and the centrifugal is a radial term, we have to use an approximated scheme. First, the Nikiforov–Uvarov (NU) method is introduced in brief, which is a systematical method, and then Schrodinger equation is solved analytically. Energy eigenvalues and the corresponding eigenvector are derived analytically by using the NU method. After that, the generalized WS potential is discussed at the end.

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 Algebraic approach to non-separable two-dimensional Schrödinger equation: Ground states for polynomial and Morse-like potentials

Open Physics ◽  
2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Vladimír Tichý ◽  
Lubomír Skála ◽  
René Hudec
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground States ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Analytic Solutions ◽  
Wave Functions ◽  
Two Dimensional ◽  
One Dimensional

AbstractThis paper presents a direct algebraic method of searching for analytic solutions of the two-dimensional time-independent Schrödinger equation that is impossible to separate into two one-dimensional ones. As examples, two-dimensional polynomial and Morse-like potentials are discussed. Analytic formulas for the ground state wave functions and the corresponding energies are presented. These results cannot be obtained by another known method.

Superstatistics and canonical quantization of the damped harmonic oscillator

2019 ◽  
Vol 34 (14) ◽  
pp. 1950108 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Thermodynamic Properties ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Canonical Quantization ◽  
Quantization Method ◽  
Dirac Delta ◽  
Energy Eigenvalues ◽  
Damped Harmonic Oscillator ◽  
Gamma Distributions

In this paper, we investigate the behavior of the energy eigenvalues of the Schrödinger equation by using the canonical quantization method. We obtain the Hamiltonian of the Schrödinger equation by the Lagrangian in terms of the new coordinates. Then we calculate the partition function by the eigenvalues and the thermodynamic properties of the system in the superstatistics formalism for the modified Dirac delta and the Gamma distributions. All results in the limiting cases satisfy that of the harmonic oscillator. Furthermore, the effects of the all parameters in the problem of energy eigenvalues and thermodynamic properties are calculated and shown graphically.

scholarly journals Approximate Solution of Schrödinger Equation with Pseudo-Gaussian Potential Viewed as a Perturbation

2015 ◽  
Vol 58 (1) ◽  
pp. 7-13
Author(s):  
Theodor-Felix Iacob ◽  
Marina Lute ◽  
Felix Iacob
Keyword(s):  
Approximate Solution ◽  
Power Series ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Additional Term ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Gaussian Potential

Abstract We consider the Schrödinger equation with pseudo-Gaussian potential and point out that it is basically made up by a term representing the harmonic oscillator potential and an additional term, which is actually a power series that converges rapidly. Based on this observation the system can be considered as a perturbation of harmonic oscillator. The perturbation method is used to approximate the energy levels of pseudo- Gaussian oscillator. The results are compared with those obtained in the analytic and numeric case.

scholarly journals Quantization of the one-dimensional free harmonic oscillator as an example of the application of the node theorem and the Macdonald-Hylleraas-Undheim theorem

2020 ◽  
Vol 22 (1) ◽  
pp. 87-90
Author(s):  
Kunle Adegoke ◽  
A. Olatinwo
Keyword(s):  
Differential Equation ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Hermite Polynomials ◽  
Traditional Methods ◽  
One Dimensional ◽  
Energy Eigenvalues ◽  
The One

Using heuristic arguments alone, based on the properties of the  wavefunctions, the energy eigenvalues and the corresponding eigenfunctions of the one-dimensional harmonic oscillator are obtained. This approach is considerably simpler and is perhaps more intuitive than the traditional methods of solving a differential equation and manipulating operators. Keywords: Time-independent Schrödinger equation, MacDonald-Hylleraas-Undheim theorem, Node theorem, Hermite polynomials,  energy eigenvalues

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