Toward chemical applications of Heaviside Operational Ansatz: exact solution of radial Schrodinger equation for nonrelativistic N-particle system with pairwise $${\frac{1}{r_{ij}}}$$ radial potential in quantum phase space

2008 ◽  
Vol 45 (1) ◽  
pp. 129-140 ◽  
Author(s):  
Valentino A. Simpao
Keyword(s):  
Exact Solution ◽  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Particle System ◽  
Quantum Phase ◽  
Radial Schrödinger Equation ◽  
Radial Potential

Contracted Schrödinger equation in quantum phase-space

2017 ◽  
Vol 39 (17) ◽  
pp. 1068-1075
Author(s):  
Carol Frishberg ◽  
Leon Cohen
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Quantum Phase

Exact solution of D-dimensional Schrödinger equation generated from certain central power-law potentials

Open Physics ◽  
2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Nabaratna Bhagawati
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Power Law ◽  
Schrodinger Equation ◽  
Transformation Method ◽  
Angular Momentum Quantum Number ◽  
Exactly Solvable Potentials ◽  
Radial Schrödinger Equation ◽  
Exactly Solvable ◽  
The Given

AbstractBy applying Extended Transformation method we have generated exact solution of D-dimensional radial Schrödinger equation for a set of power-law multi-term potentials taking singular potentials $$V(r) = ar^{ - \tfrac{1} {2}} + br^{ - \tfrac{3} {2}}$$, $$V(r) = ar^{\tfrac{2} {3}} + br^{ - \tfrac{2} {3}} + cr^{ - \tfrac{4} {3}}$$, V(r) = ar + br −1 + cr 2 and V(r) = ar 2+br −2+cr −4+dr −6 as input reference. The restriction on the parameters of the given potentials and angular momentum quantum number ℓ are obtained. The multiplet structure of the generated exactly solvable potentials are also shown.

scholarly journals Exact Solution of Schrödinger Equation with Inverted Woods-Saxon and Manning-Rosen Potentials

2010 ◽  
Vol 3 (1) ◽  
pp. 25 ◽  
Author(s):  
A. N. Ikot ◽  
L. E. Akpabio ◽  
E. B. Umoren
Keyword(s):  
Exact Solution ◽  
Wave Function ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Negative Energy ◽  
Dinger Equation ◽  
Radial Schrödinger Equation ◽  
Rosen Potential

We have analytically solved the radial Schrödinger equation with inverted Woods-Saxon and Manning-Rosen Potentials. With the ansatz for the wave function, we obtain the generalized wave function and the negative energy spectrum for the system.Keywords: Inverted Woods-Saxon Potentials; Manning-Rosen Potential; Schrödinger Equation.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i1.5310                J. Sci. Res. 3 (1), 25-33 (2011)

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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