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.

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.

THE FERMION-FERMION EFFECTIVE ACTION FOR THE THREE-DIMENSIONAL MASSIVE THIRRING MODEL

1994 ◽  
Vol 09 (18) ◽  
pp. 3143-3151 ◽  
Author(s):  
R.F. RIBEIRO ◽  
E.R. BEZERRA DE MELLO
Keyword(s):  
Schrödinger Equation ◽  
Effective Potential ◽  
Effective Action ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Bound State ◽  
Thirring Model ◽  
Coupling Constant ◽  
Massive Thirring Model

In this paper a nonrelativistic fermion-fermion effective potential for a three-dimensional massive Thirring model is obtained in a 1/N expansion. We show, by analyzing the Schrödinger equation in the presence of this potential, that the system presents a fermion-fermion bound state for a positive value of the coupling constant g.

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.

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.

Curvilinear coordinate lattice Boltzmann simulation for necklace-ring beams in the nonlinear Schrödinger equation

2020 ◽  
Vol 31 (10) ◽  
pp. 2050136
Author(s):  
Boyu Wang ◽  
Jianying Zhang ◽  
Guangwu Yan
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Lattice Boltzmann ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Time Derivative ◽  
Three Dimensional ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Curvilinear Coordinate

Necklace-ring solitons have gained much attention due to their potential applications in optics and other scientific areas. In this paper, the numerical investigation of the nonlinear Schrödinger equation by using the curvilinear coordinate lattice Boltzmann method is proposed to study necklace-ring solitons. Different from those used in the general curvilinear coordinate lattice Boltzmann models, the lattices used in this work are uniform in two- and three-dimensional space. Furthermore, the model contains spatial evolution rather than time evolution to avoid the complexity of dealing with higher-order time derivative terms as well as to maintain the simplicity of the algorithm. Numerical experiments reproduce the evolution of two- and three-dimensional necklace-ring solitons. The truncation error analysis indicates that our model is equivalent to the Crank–Nicolson difference scheme.

scholarly journals Some topics in differential geometry of normed spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Vitor Balestro ◽  
Horst Martini ◽  
Ralph Teixeira
Keyword(s):  
Differential Geometry ◽  
Minimal Surfaces ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Inner Product ◽  
Normed Spaces ◽  
Smooth Norm ◽  
Bonnet Theorem ◽  
Three Dimensional Space

AbstractFor a surface immersed in a three-dimensional space endowed with a smooth norm instead of an inner product, one can define analogous concepts of curvature and metric. With such concepts in mind, various questions immediately appear. The aim of this paper is to propose and answer some of those questions. In this framework we prove several characterizations of minimal surfaces in normed spaces, and respective analogues of some global theorems (e.g., Hadamard-type theorems) are also derived. A result on the curvature of surfaces having constant Minkowskian width is given, and finally we study the ambient metric induced on the surface, proving an extension of the classical Bonnet theorem.

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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