Study of Schrodinger Equation with Quantum Deformation for Three-Dimensional Harmonic Oscillator plus Inverse Quadratic Potential by Hypergeometric Method

2019 ◽  
Vol 8 (6) ◽  
pp. 2788-2793 ◽  
Author(s):  
Dyah Ayu Dianawati ◽  
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Quantum Deformation ◽  
Quadratic Potential

scholarly journals Generation of Time-Independent and Time-Dependent Harmonic Oscillator-Like Potentials Using Supersymmetric Quantum Mechanics

2018 ◽  
Vol 4 (1) ◽  
pp. 47-55
Author(s):  
Timothy Brian Huber
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Mechanical System ◽  
Schrodinger Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Intertwining Operator

The harmonic oscillator is a quantum mechanical system that represents one of the most basic potentials. In order to understand the behavior of a particle within this system, the time-independent Schrödinger equation was solved; in other words, its eigenfunctions and eigenvalues were found. The first goal of this study was to construct a family of single parameter potentials and corresponding eigenfunctions with a spectrum similar to that of the harmonic oscillator. This task was achieved by means of supersymmetric quantum mechanics, which utilizes an intertwining operator that relates a known Hamiltonian with another whose potential is to be built. Secondly, a generalization of the technique was used to work with the time-dependent Schrödinger equation to construct new potentials and corresponding solutions.

Diverse bistable dark novel explicit wave solutions of cubic–quintic nonlinear Helmholtz model

2021 ◽  
pp. 2150441
Author(s):  
Mostafa M. A. Khater
Keyword(s):  
Solitary Wave ◽  
Schrödinger Equation ◽  
General Model ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Solitary Wave Solutions ◽  
Computational Schemes ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

This paper examines three different recent computational schemes (extended simplest equation (ESE) method, modified Kudryashov (MKud) method, and modified Khater (MKha) method) for obtaining novel solitary wave solutions of cubic–quintic nonlinear Helmholtz (CQ–NLH) model. This model is considered as a general model of the well-known Schrödinger equation where it takes into account the effects of backward scattering that are neglected in the more common nonlinear Schrödinger model. Many distinct wave solutions are explained in the different formulas, such as trigonometric, rational, and hyperbolic formulas. These solutions are described in some precise sketches in two- and three-dimensional. The methods’ performance is explained to demonstrate their effectiveness and power.

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