Approximate analytical solutions and mean energies of stationary Schrödinger equation for the general molecular potential

2021 ◽  
Author(s):  
Eyube E. S ◽  
Rawen B O ◽  
Ibrahim N
Keyword(s):  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Stationary Schrödinger Equation ◽  
Molecular Potential ◽  
Approximate Analytical Solutions

scholarly journals SEMIRELATIVISTIC HAMILTONIANS AND THE AUXILIARY FIELD METHOD

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4695-4726 ◽  
Author(s):  
BERNARD SILVESTRE-BRAC ◽  
CLAUDE SEMAY ◽  
FABIEN BUISSERET
Keyword(s):  
Schrödinger Equation ◽  
Power Law ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Field Method ◽  
Auxiliary Field ◽  
Square Root ◽  
Exact Results ◽  
Approximate Analytical Solutions ◽  
Envelope Theory

Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form [Formula: see text] are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope theory, has been recently proposed as a powerful tool to get approximate analytical solutions of the Schrödinger equation. Various shapes for the potential V(r) are investigated: power-law, funnel, square root, and Yukawa. A comparison with the exact results is discussed in detail.

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

Sign in / Sign up

Export Citation Format

Share Document