Particular solutions of the radial Schrödinger equation via Nabla discrete fractional calculus operator

2017 ◽  
Author(s):  
Okkes Ozturk ◽  
Resat Yilmazer
Keyword(s):  
Schrödinger Equation ◽  
Fractional Calculus ◽  
Schrodinger Equation ◽  
Discrete Fractional Calculus ◽  
Particular Solutions ◽  
Radial Schrödinger Equation

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.

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

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