Discrete fractional solutions of radial Schrödinger equation for Makarov potential

2017 ◽  
Vol 20 (03) ◽  
pp. 1750019 ◽  
Author(s):  
Okkes Ozturk
Keyword(s):  
Schrödinger Equation ◽  
Fractional Calculus ◽  
Schrodinger Equation ◽  
Arbitrary Order ◽  
Applied Mathematics ◽  
Discrete Mathematics ◽  
Discrete Fractional Calculus ◽  
Science And Engineering ◽  
Finite Structures ◽  
Radial Schrödinger Equation

The fractional calculus that is a theory of integral and derivative with arbitrary order is an important subject of applied mathematics. This theory has extensive usage fields in science and engineering. Discrete mathematics, the study of finite structures, is one of the fastest growing areas in mathematics and optimization. Recently, many considerable scientific works were published on fractional calculus and discrete fractional calculus (DFC). The purpose of this paper is to obtain discrete fractional solutions of radial Schrödinger equation for Makarov potential by means of nabla DFC operator. Moreover, we introduce hypergeometric forms of these solutions.

scholarly journals Wavelet Methods for Solving Fractional Order Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
A. K. Gupta ◽  
S. Saha Ray
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Fractional Differential Equations ◽  
Arbitrary Order ◽  
Applied Mathematics ◽  
Science And Engineering ◽  
The Past ◽  
Biological Population ◽  
Fractional Differential ◽  
Wavelet Methods

Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linear and nonlinear fractional differential equations. Our goal is to analyze the selected wavelet methods and assess their accuracy and efficiency with regard to solving fractional differential equations. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on various wavelets in order to solve differential equations of arbitrary order.

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.

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