The energy levels of the Schrodinger equation for various types of potentials using a renormalized method

1991 ◽  
Vol 24 (13) ◽  
pp. 3041-3051 ◽  
Author(s):  
M R M Witwit
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels

Approximate analytical solution of continuous states for the l-wave Schrödinger equation with a diatomic molecule potential

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Gao-Feng Wei ◽  
Wen-Chao Qiang ◽  
Wen-Li Chen
Keyword(s):  
Schrödinger Equation ◽  
Diatomic Molecule ◽  
Schrodinger Equation ◽  
Scattering Amplitude ◽  
Energy Levels ◽  
Bound State ◽  
Radial Wave ◽  
Continuous States ◽  
Analytical Properties ◽  
Function Potential

AbstractThe continuous states of the l-wave Schrödinger equation for the diatomic molecule represented by the hyperbolical function potential are carried out by a proper approximation scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Schrödinger equation for the hyperbolical function potential are presented and the corresponding calculation formula of phase shifts is derived. Also, we interestingly obtain the corresponding bound state energy levels by analyzing analytical properties of scattering amplitude.

scholarly journals THE q-DEFORMED SCHRÖDINGER EQUATION OF THE HARMONIC OSCILLATOR ON THE QUANTUM EUCLIDEAN SPACE

1994 ◽  
Vol 09 (22) ◽  
pp. 3989-4008 ◽  
Author(s):  
URSULA CAROW-WATAMURA ◽  
SATOSHI WATAMURA
Keyword(s):  
Euclidean Space ◽  
Difference Equation ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Series Representation ◽  
Exponential Functions ◽  
Creation And Annihilation Operators ◽  
The Creation

We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.

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 Solusi Persamaan Schrödinger untuk Potensial Hulthen + Non-Sentral Poschl-Teller dengan Menggunakan Metode Nikiforov-Uvarov

2016 ◽  
Vol 3 (02) ◽  
pp. 169
Author(s):  
Nani Sunarmi ◽  
Suparmi S ◽  
Cari C
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Energy Levels ◽  
Hulthén Potential ◽  
Central Potential ◽  
Hulthen Potential ◽  
Hypergeometric Type ◽  
Angular Equation ◽  
Uvarov Method

<span>The Schrödinger equation for Hulthen potential plus Poschl-Teller Non-Central potential is <span>solved analytically using Nikiforov-Uvarov method. The radial equation and angular equation <span>are obtained through the variable separation. The solving of Schrödinger equation with <span>Nikivorov-Uvarov method (NU) has been done by reducing the two order differensial equation <span>to be the two order differential equation Hypergeometric type through substitution of <span>appropriate variables. The energy levels obtained is a closed function while the wave functions <span>(radial and angular part) are expressed in the form of Jacobi polynomials. The Poschl-Teller <span>Non-Central potential causes the orbital quantum number increased and the energy of the <span>Hulthen potential is increasing positively.</span></span></span></span></span></span></span></span><br /></span>

scholarly journals On the Use of B-Splines as Ritz Variational Basis Functions to Solve the Schrodinger Equation (TISE) for a constrained free Quantum Particle

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Anandaram Mandyam N
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Quantum Particle ◽  
Bernstein Polynomials ◽  
Energy Levels ◽  
Basis Functions ◽  
Spline Collocation ◽  
Stationary Schrödinger Equation ◽  
B Splines ◽  
Domain Length

B-Splines as piecewise adaptation of Bernstein polynomials (aka, B-polys) are widely used as Ritz variational basis functions in solving many problems in the fields of quantum mechanics and atomic physics. In this paper they are used to solve the 1-D stationary Schrodinger equation (TISE) for a free quantum particle subject to a fixed domain length by using the Python software SPLIPY with different sets of computation parameters. In every case it was found that over 60 percent of energy levels had excellent accuracy thereby proving that the use of B-spline collocation is a preferred method.

Parabolic band approximation of the electron energy levels in a tetrahedral-shaped quantum dot

2008 ◽  
Vol 86 (11) ◽  
pp. 1327-1331
Author(s):  
T Pengpan ◽  
C Daengngam
Keyword(s):  
Quantum Dot ◽  
Schrödinger Equation ◽  
Effective Mass ◽  
Electron Energy ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Nonlinear Schrodinger Equation ◽  
Gradient Term ◽  
Nonlinear Schrödinger

In more elaborate schemes, an electron’s effective mass in a heterostructure semiconductor quantum dot (QD) depends on both its position and its energy. However, the electron’s effective mass can be simply modeled by a parabolic band approximation — the electron’s effective mass inside the QD — which is assumed to be constant and differs from the one outside the QD, which is also assumed to be constant. The governing equation to be solved for the electron’s energy levels inside the QD is the nonlinear Schrödinger equation. With the approximation, the nonlinear Schrödinger equation for a tetrahedral-shaped QD is discretized by using the finite-volume method. The discretized nonlinear Schrödinger equation is solved for the electron energy levels by a computer program. It is noted that the resulting energy levels for the parabolic mass model are nondegenerate due to the mass-gradient term at the corners, edges, and surfaces of the tetrahedral-shaped QD.PACS Nos.: 02.60.Cb, 03.65.Ge, 81.07.Ta

The energy levels of ‘holes’ in liquids

1945 ◽  
Vol 41 (2) ◽  
pp. 180-183 ◽  
Author(s):  
F. C. Auluck ◽  
D. S. Kothari
Keyword(s):  
Surface Tension ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Hole Theory ◽  
Theory Of Liquids

SummaryThe Schrödinger equation for a ‘hole’ in the hole-theory of liquids is constructed and solved by the B.W.K. method. The energy levels are found to be discrete, and the eigenvalues are obtained in terms of the density and surface tension of the liquid. The relation between the energy of the ground state and the temperature of melting is considered.

A new determination of the parameters of the optimized Heine–Abarenkov potential for 27 elements

1976 ◽  
Vol 54 (23) ◽  
pp. 2348-2354 ◽  
Author(s):  
E. R. Cowley
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Inhomogeneity Correction ◽  
Radial Schrödinger Equation

We have calculated the energy levels of the truncated Coulomb potential using numerical integration of the radial Schrödinger equation, rather than interpolation in tables. The results are used to give the parameters of the optimized Heine–Abarenkov potential for 27 elements. Various methods of weighting other contributions to the potential in the solid are used, and the inhomogeneity correction introduced by Ballentine and Gupta is discussed.

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