Energy levels of the Schrödinger equation for some rational potentials in two-dimensional space using the inner product technique

Pramana ◽  
1994 ◽  
Vol 43 (4) ◽  
pp. 279-287 ◽  
Author(s):  
M R M Witwit ◽  
J P Killingbeck
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Energy Levels ◽  
Inner Product ◽  
Two Dimensional ◽  
Product Technique

A Hill-determinant approach to symmetric double-well potentials in two dimensions

1995 ◽  
Vol 73 (9-10) ◽  
pp. 632-637 ◽  
Author(s):  
M. R. M. Witwit ◽  
J. P. Killingbeck
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Energy Levels ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Degenerate Eigenvalues ◽  
Double Well Potential ◽  
Range Of Values

Energy levels of the Schrödinger equation for a double-well potential V(x,y;Z2,λ) = −Z2[x2 + y2] + λ[axxx4 + 2axyx2y2 + ayyy4] in two-dimensional space are calculated, using a Hill-determinant approach for several eigenstates and a range of values of λ and Z2. Special emphasis is placed on the larger values of Z2, for which the eigenvalues for different states have almost degenerate eigenvalues.

Quasi-bound state calculations for several types of potential in one-, two-, and three-dimensional systems, using perturbative techniques

1993 ◽  
Vol 71 (3-4) ◽  
pp. 133-141 ◽  
Author(s):  
M. R. M. Witwit
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Energy Levels ◽  
Three Dimensional ◽  
Bound State ◽  
Inner Product ◽  
Model Potentials ◽  
Three Dimensional Space ◽  
Quasi Bound State

The energy levels of the Schrödinger equation for various model potentials in one-, two-, and three-dimensional space are calculated using the hypervirial and inner product methods.

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.

scholarly journals Exact Noncommutative Two-Dimensional Hydrogen Atom

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
B. C. Wang ◽  
E. C. Brenag ◽  
R. G. G. Amorim ◽  
V. C. Rispoli ◽  
S. C. Ulhoa
Keyword(s):  
Experimental Data ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Two Dimensional ◽  
Exact Analysis

In this work, we present an exact analysis of the two-dimensional noncommutative hydrogen atom. In this study, the Levi-Civita transformation was used to perform the solution of the noncommutative Schrodinger equation for Coulomb potential. As an important result, we determine the energy levels for the considered system. Using the result obtained and experimental data, a bound on the noncommutativity parameter was obtained.

A Dynamic Adaptive Wavelet Method for Solution of the Schrodinger Equation

2015 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
Ratikanta Behera ◽  
Mani Mehra
Keyword(s):  
Schrödinger Equation ◽  
Computational Efficiency ◽  
Schrodinger Equation ◽  
Computational Cost ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
One Dimensional ◽  
Grid Adaptation ◽  
Adaptive Wavelet Method

In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based on spherical wavelet over an optimal spherical geodesic grid. The method is applied to the solution of Schrodinger equation for computational efficiency and achieve accuracy with controlling spatial grid adaptation — high resolution computations are performed only in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Thereupon the dynamic adaptive wavelet method is useful to analyze local structure of solution with very less number of computational cost than any other methods. The prowess and computational efficiency of the adaptive wavelet method is demonstrated for the solution of Schrodinger equation on one-dimensional, two-dimensional and on the sphere.

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