Function space requirements for the single-electron functions within the multiparticle Schrödinger equation

2013 ◽  
Vol 54 (6) ◽  
pp. 062105 ◽  
Author(s):  
Martin J. Mohlenkamp
Keyword(s):  
Schrödinger Equation ◽  
Function Space ◽  
Schrodinger Equation ◽  
Single Electron ◽  
Space Requirements

THE THEORY OF AN ELECTRON ON A LOXODROME

2012 ◽  
Vol 26 (08) ◽  
pp. 1250052 ◽  
Author(s):  
DAVID S. TOURIGNY
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Single Electron ◽  
Molecular Physics ◽  
Helical Polymers ◽  
Quantum Properties ◽  
Electron Models ◽  
Apple Peels

Single-electron models are regularly used in molecular physics to obtain information on the quantum properties of many-atom systems. Examples include applications of a particle contained on a ring to benzene, and an electron on a helix to helical polymers. Here it is shown that the model of an electron on a spherical helix (a loxodrome) is also amenable to such investigation, and may be used to describe an emerging class of molecules known as "molecular apple peels". Moreover, the Schrödinger equation that arises during consideration of this model is solved exactly.

scholarly journals The Analytical Solutions of the Schrodinger Equation for a Single Electron in the Nikiforov-Uvarov Framework

Jurnal Fisika ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 1-10
Author(s):  
Yacobus Yulianto ◽  
Zaki Su'ud
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Quantum Physics ◽  
Energy Eigenvalue ◽  
Single Electron ◽  
Alternative Procedure ◽  
Alternative Method ◽  
Uvarov Method

In this study, it is intended to show an alternative method to derive the wave function of a single electron as solutions of the Schrodinger equation. The Nikiforov-Uvarov method was chosen to be utilized since this method can solve the Schrodinger equation with several well-known potentials in the non-relativistic mechanics of quantum. The obtained results of this study have succeed to explain the wave function and the energy eigenvalue for a single electron as lectured in quantum physics textbooks. These results prove that the Nikiforov-Uvarov method provides an alternative procedure to solve the Schrodinger equation.

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

Introduction

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
State Level ◽  
Boltzmann Distribution ◽  
Theoretical Description ◽  
Time Dependent ◽  
Nuclear Dynamics ◽  
Molecular Reaction ◽  
Oppenheimer Approximation

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized state-to-state level is discussed. The theoretical description of these reactions based on the time-dependent Schrödinger equation and the Born–Oppenheimer approximation is introduced and the resulting time-dependent Schrödinger equation describing the nuclear dynamics is discussed. The chapter concludes with a brief discussion of matter at thermal equilibrium, focusing at the Boltzmann distribution. Thus, the Boltzmann distribution for vibrational, rotational, and translational degrees of freedom is discussed and illustrated.

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