scholarly journals ALGEBRAIC APPROACH TO THE SPECTRAL PROBLEM FOR THE SCHRÖDINGER EQUATION WITH POWER POTENTIALS

2000 ◽  
Vol 15 (02) ◽  
pp. 209-226 ◽  
Author(s):  
R. N. FAUSTOV ◽  
V. O. GALKIN ◽  
A. V. TATARINTSEV ◽  
A. S. VSHIVTSEV
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mass Spectra ◽  
Infinite System ◽  
Algebraic Approach ◽  
Heavy Quarkonium ◽  
Algebraic Equations ◽  
Cornell Potential ◽  
Relativistic Equations ◽  
Good Agreement

The method reducing the solution of the Schrödinger equation for several types of power potentials to the solution of the eigenvalue problem for the infinite system of algebraic equations is developed. The finite truncation of this system provides high accuracy results for low-lying levels. The proposed approach is appropriate both for analytic calculations and for numerical computations. This method allows also to determine the spectrum of the Schrödinger-like relativistic equations. The heavy quarkonium (charmonium and bottomonium) mass spectra for the Cornell potential and the sum of the Coulomb and oscillator potentials are calculated. The results are in good agreement with experimental data.

scholarly journals Study on the Applicability of Varshni Potential to Predict the Mass Spectra of the Quark-Antiquark Systems in a Non-relativistic Framework

2021 ◽  
Vol 14 (4) ◽  
pp. 339-347
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mass Spectra ◽  
Laguerre Polynomials ◽  
Heavy Meson ◽  
Energy Eigenvalues ◽  
Relativistic Regime ◽  
Uvarov Method ◽  
Relativistic Framework ◽  
Good Agreement

Abstract: In this work, we obtain the Schrödinger equation solutions for the Varshni potential using the Nikiforov-Uvarov method. The energy eigenvalues are obtained in non-relativistic regime. The corresponding eigenfunction is obtained in terms of Laguerre polynomials. We applied the present results to calculate heavy-meson masses of charmonium cc ¯ and bottomonium bb ¯. The mass spectra for charmonium and bottomonium multiplets have been predicted numerically. The results are in good agreement with experimental data and the works of other researchers. Keywords: Schrödinger equation, Varshni potential, Nikiforov-Uvarov method, Heavy meson. PACs: 14.20.Lq; 03.65.-w; 14.40.Pq; 11.80.Fv.

scholarly journals Cornell Potential: A Neural Network Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Halil Mutuk
Keyword(s):  
Neural Network ◽  
Experimental Data ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Linear Potential ◽  
Network Approach ◽  
Neural Network Approach ◽  
Cornell Potential ◽  
Potential Parameters ◽  
Good Agreement

We solved Schrödinger equation with Cornell potential (Coulomb-plus-linear potential) by using neural network approach. Four different cases of Cornell potential for different potential parameters were used without a physical relevance. Besides that charmonium, bottomonium and bottom-charmed spin-averaged spectra were also calculated. Obtained results are in good agreement with the reference studies and available experimental data.

EXACT SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH SPHERICALLY SYMMETRIC OCTIC POTENTIAL

2012 ◽  
Vol 27 (20) ◽  
pp. 1250112 ◽  
Author(s):  
DAVIDS AGBOOLA ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Spherically Symmetric ◽  
Algebraic Equations ◽  
Potential Parameters

We present exact solutions of the Schrödinger equation with spherically symmetric octic potential. We give closed-form expressions for the energies and the wave functions as well as the allowed values of the potential parameters in terms of a set of algebraic equations.

ARBITRARY l-WAVE SOLUTIONS OF THE SCHRÖDINGER EQUATION FOR THE SCREEN COULOMB POTENTIAL

2013 ◽  
Vol 22 (06) ◽  
pp. 1350036 ◽  
Author(s):  
SHISHAN DONG ◽  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
State Energy ◽  
Energy Levels ◽  
Bound State ◽  
Screen Coulomb Potential ◽  
Normalization Constant ◽  
Angular Momentum State ◽  
Good Agreement

Using improved approximate schemes for centrifugal term and the singular factor 1/r appearing in potential itself, we solve the Schrödinger equation with the screen Coulomb potential for arbitrary angular momentum state l. The bound state energy levels are obtained. A closed form of normalization constant of the wave functions is also found. The numerical results show that our results are in good agreement with those obtained by other methods. The key issue is how to treat two singular points in this quantum system.

scholarly journals Diatomic Molecules and Mass Spectrum of Heavy Quarkonium System with Kratzer- Screened Coulomb Potential (KSCP) through the Solutions of the Schrödinger Equation

2021 ◽  
Vol 3 (2) ◽  
pp. 48-55
Author(s):  
E. P. Inyang ◽  
E. P. Inyang ◽  
J. Karniliyus ◽  
J. E. Ntibi ◽  
E. S. William
Keyword(s):  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Diatomic Molecules ◽  
Expansion Method ◽  
Bound State ◽  
Heavy Quarkonium ◽  
Energy Eigenvalues ◽  
Special Cases ◽  
Screened Coulomb Potential

In this work, we obtain solutions of the Schrödinger equation with Kratzer-screened Coulomb potential (KSCP) model using the series expansion method. Explicitly, we compute the bound state energy eigenvalues for selected diatomic molecules of N2, CO, NO, and CH, respectively, for the various vibrational and rotational quantum states and the numerical energy eigenvalues agree with the existing literature. Three special cases were considered. The energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium system such as charmonium and bottomonium. The results agree with the experimental data and other recent theoretical studies.

SUPER-RECURRENCE PHENOMENON RELEVANT TO THE PHASE IN THE NONLINEAR SCHRÖDINGER EQUATION

1995 ◽  
Vol 09 (17) ◽  
pp. 1045-1052 ◽  
Author(s):  
Y. YANG ◽  
Y. TAN ◽  
W.Y. ZHANG ◽  
C.Y. ZHENG
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Boundary Conditions ◽  
Nonlinear Schrodinger Equation ◽  
Initial Condition ◽  
Nonlinear Schrödinger ◽  
Recurrence Period ◽  
Spatially Periodic ◽  
Good Agreement

The nonlinear Schrödinger equation with spatially periodic boundary conditions is numerically solved by means of the spectrum method. It is found that with the initial condition carefully chosen, the phase recurrence just appears when the amplitudes have the nineteenth recurrences to the initial condition. This phenomenon is called as the phase super-recurrence. Using a simple perturbation model, the amplitude recurrence period Ta and the phase change ∆φa in the period Ta are estimated, and a good agreement between this estimation and the numerical results of the nonlinear Schrödinger equation is shown.

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.

ALGEBRAIC APPROACH TO THE PSEUDOHARMONIC OSCILLATOR IN 2D

2002 ◽  
Vol 11 (02) ◽  
pp. 155-160 ◽  
Author(s):  
SHI-HAI DONG ◽  
ZHONG-QI MA
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Algebraic Approach ◽  
Matrix Elements ◽  
Ladder Operators ◽  
Commutation Relations ◽  
The Matrix ◽  
Pseudoharmonic Oscillator ◽  
Analytical Expressions

A realization of the ladder operators for the solutions to the Schrödinger equation with a pseudoharmonic oscillator in 2D is presented. It is shown that those operators satisfy the commutation relations of an SU(1, 1) algebra. Closed analytical expressions are evaluated for the matrix elements of some operators r2 and r∂/∂ r

scholarly journals Solutions of the Schrödinger equation for pseudo-Coulomb potential plus a new improved ring-shaped potential in the cosmic string space–time

2016 ◽  
Vol 94 (5) ◽  
pp. 517-521 ◽  
Author(s):  
Akpan N. Ikot ◽  
Tamunoimi M. Abbey ◽  
Ephraim O. Chukwuocha ◽  
Michael C. Onyeaju
Keyword(s):  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Cosmic String ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Space Time ◽  
Minkowski Space Time ◽  
Uvarov Method ◽  
Good Agreement

In this paper, we obtain the bound state energy eigenvalues and the corresponding eigenfunctions of the Schrödinger equation for the pseudo-Coulomb potential plus a new improved ring-shaped potential within the framework of cosmic string space–time using the generalized parametric Nikiforov–Uvarov method. Our results are in good agreement with other works in the cosmic string space–time and reduced to those in the Minkowski space–time when α = 1.

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.

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