A STUDY ABOUT THE SOLUTIONS OF SCHRÖDINGER EQUATION WITH AN ASYMPTOTICALLY LINEAR POTENTIAL

1996 ◽  
Vol 11 (03) ◽  
pp. 207-209 ◽  
Author(s):  
ELSO DRIGO FILHO
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
Expansion Method ◽  
Linear Potential ◽  
Asymptotically Linear

We determine the solutions of the Schrödinger equation for an asymptotically linear potential. Analytical solutions are obtained by superalgebra in quantum mechanics and we establish when these solutions are possible. Numerical solutions for the spectra are obtained by the shifted 1/N expansion method.

A GENERALIZED SUB-EQUATION EXPANSION METHOD AND ITS APPLICATION TO THE NONLINEAR SCHRÖDINGER EQUATION IN INHOMOGENEOUS OPTICAL FIBER MEDIA

2007 ◽  
Vol 18 (07) ◽  
pp. 1187-1201 ◽  
Author(s):  
BIAO LI
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Analytical Solutions ◽  
Elliptic Function ◽  
Schrodinger Equation ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Jacobi Elliptic Function ◽  
Exact Analytical Solutions ◽  
Nonlinear Schrödinger

In this paper, a generalized sub-equation expansion method is presented for constructing some exact analytical solutions of nonlinear partial differential equations. Making use of the method and symbolic computation, we investigate the inhomogeneous nonlinear Schrödinger equation (INLSE) with the loss/gain and the frequency chirping and obtain rich exact analytical solutions. From our results, many known results of some nonlinear Schrödinger equations can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. With computer simulation, the main soliton features of bright and dark solitons, Jacobi elliptic function solutions, and Weierstrass elliptic function solutions are shown by some figures. Nonlinear dynamics of the chirped soliton pulses is also investigated under the different regimes of soliton management. The method developed does provide a systematic way to generate various exact analytical solutions for INLSE with varying coefficients.

scholarly journals Using spreadsheets to teach quantum theory

2016 ◽  
pp. 16-19
Author(s):  
Kieran F Lim
Keyword(s):  
Biological Sciences ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
Special Cases ◽  
Physical And Chemical

Quantum theory is a key part of the physical and chemical sciences. Traditionally, the teaching of quantum theory has relied heavily on the use of calculus to solve the Schrödinger equation for a limited number of special cases. This approach is not suitable for students who are weak in mathematics, for example, many students who are majoring in biochemistry, biological sciences, etc.Spreadsheets generate approximate numerical solutions and graphical descriptions of the Schrödinger equation to develop a qualitative appreciation of quantum mechanics.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

A Student's Guide to the Schrödinger Equation

2020 ◽  
Author(s):  
Daniel A. Fleisch
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Plain Language ◽  
Science And Engineering ◽  
Popular Approach ◽  
Matlab Code ◽  
Mathematical Techniques

Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schrödinger equation and to analyze the resulting wave functions. Retaining the popular approach used in Fleisch's other Student's Guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schrödinger equation in quantum mechanics. It addresses in a clear and intuitive way the problems students find most troublesome. Each chapter includes several homework problems with fully worked solutions. A companion website hosts additional resources, including a helpful glossary, Matlab code for creating key simulations, revision quizzes and a series of videos in which the author explains the most important concepts from each section of the book.

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.

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