scholarly journals The Schrödinger Equation, the Zero-Point Electromagnetic Radiation, and the Photoelectric Effect

2016 ◽  
Vol 46 (2) ◽  
pp. 184-191
Author(s):  
H. M. França ◽  
A. Kamimura ◽  
G. A. Barreto
Keyword(s):  
Schrödinger Equation ◽  
Electromagnetic Radiation ◽  
Schrodinger Equation ◽  
Zero Point ◽  
Photoelectric Effect

scholarly journals Simplistic calculation of the tunneling splittings for proton transfer in malonaldehyde and formic acid dimer using the one-dimensional Schrödinger equation

2021 ◽  
Author(s):  
Denis S. Tikhonov
Keyword(s):  
Schrödinger Equation ◽  
Proton Transfer ◽  
Formic Acid ◽  
Schrodinger Equation ◽  
Zero Point ◽  
Basis Set ◽  
One Dimensional ◽  
Hartree Fock ◽  
Tunneling Splittings ◽  
Complete Basis Set

Abstract In this manuscript we present an approach for computing tunneling splittings for large amplitude motions. The core of the approach is a solution of an effective one-dimensional Schrödinger equation with an effective mass and an effective potential energy surface composed of electronic and harmonic zero-point vibrational energies of small amplitude motions in the molecule. The method has been shown to work in cases of three model motions: nitrogen inversion in ammonia, single proton transfer in malonaldehyde, and double proton transfer in the formic acid dimer. In the current work we also investigate the performance of different DFT and post-Hartree-Fock methods for prediction of the proton transfer tunneling splittings, quality of the effective Schrödinger equation parameters upon the isotopic substitution, and possibility of a complete basis set (CBS) extrapolation for the resulting tunneling splittings.

scholarly journals A simplistic computational procedure for tunneling splittings caused by proton transfer

2021 ◽  
Author(s):  
Denis S. Tikhonov
Keyword(s):  
Schrödinger Equation ◽  
Proton Transfer ◽  
Schrodinger Equation ◽  
Zero Point ◽  
Computational Procedure ◽  
Basis Set ◽  
Hartree Fock ◽  
Tunneling Splittings ◽  
Complete Basis Set ◽  
Large Amplitude Motions

AbstractIn this manuscript, we present an approach for computing tunneling splittings for large amplitude motions. The core of the approach is a solution of an effective one-dimensional Schrödinger equation with an effective mass and an effective potential energy surface composed of electronic and harmonic zero-point vibrational energies of small amplitude motions in the molecule. The method has been shown to work in cases of three model motions: nitrogen inversion in ammonia, single proton transfer in malonaldehyde, and double proton transfer in the formic acid dimer. In the current work, we also investigate the performance of different DFT and post-Hartree–Fock methods for prediction of the proton transfer tunneling splittings, quality of the effective Schrödinger equation parameters upon the isotopic substitution, and possibility of a complete basis set (CBS) extrapolation for the resulting tunneling splittings.

scholarly journals Accurate Tunneling Splittings for Proton Transfer in Malonaldehyde and Formic Acid Dimer Using the One-Dimensional Schrödinger Equation

2021 ◽  
Author(s):  
Denis Tikhonov
Keyword(s):  
Schrödinger Equation ◽  
Proton Transfer ◽  
Formic Acid ◽  
Schrodinger Equation ◽  
Zero Point ◽  
Basis Set ◽  
One Dimensional ◽  
Hartree Fock ◽  
Tunneling Splittings ◽  
Complete Basis Set

In this manuscript we present an approach for computing tunneling splittings for large amplitude motions. <br>The core of the approach is a solution of an effective one-dimensional Schrödinger equation with an effective mass and an effective potential energy surface composed of electronic and harmonic zero-point vibrational energies of small amplitude motions in the molecule.<br>The method has been shown to work in cases of three model motions: nitrogen inversion in ammonia, single proton transfer in malonaldehyde, and double proton transfer in the formic acid dimer. In the current work we also investigate the performance of different DFT and post-Hartree-Fock methods for prediction of the proton transfer tunneling splittings, quality of the effective Schrödinger equation parameters upon the isotopic substitution, and possibility of a complete basis set (CBS) extrapolation for the resulting tunneling splittings.<br>

scholarly journals Accurate Tunneling Splittings for Proton Transfer in Malonaldehyde and Formic Acid Dimer Using the One-Dimensional Schrödinger Equation

2021 ◽  
Author(s):  
Denis Tikhonov
Keyword(s):  
Schrödinger Equation ◽  
Proton Transfer ◽  
Formic Acid ◽  
Schrodinger Equation ◽  
Zero Point ◽  
Basis Set ◽  
One Dimensional ◽  
Hartree Fock ◽  
Tunneling Splittings ◽  
Complete Basis Set

In this manuscript we present an approach for computing tunneling splittings for large amplitude motions. <br>The core of the approach is a solution of an effective one-dimensional Schrödinger equation with an effective mass and an effective potential energy surface composed of electronic and harmonic zero-point vibrational energies of small amplitude motions in the molecule.<br>The method has been shown to work in cases of three model motions: nitrogen inversion in ammonia, single proton transfer in malonaldehyde, and double proton transfer in the formic acid dimer. In the current work we also investigate the performance of different DFT and post-Hartree-Fock methods for prediction of the proton transfer tunneling splittings, quality of the effective Schrödinger equation parameters upon the isotopic substitution, and possibility of a complete basis set (CBS) extrapolation for the resulting tunneling splittings.<br>

scholarly journals Simplistic calculation of the tunneling splittings for proton transfer in malonaldehyde and formic acid dimer using the one-dimensional Schrödinger equation

2021 ◽  
Author(s):  
Denis Tikhonov
Keyword(s):  
Schrödinger Equation ◽  
Proton Transfer ◽  
Formic Acid ◽  
Schrodinger Equation ◽  
Zero Point ◽  
Basis Set ◽  
One Dimensional ◽  
Hartree Fock ◽  
Tunneling Splittings ◽  
Complete Basis Set

In this manuscript we present an approach for computing tunneling splittings for large amplitude motions. <br>The core of the approach is a solution of an effective one-dimensional Schrödinger equation with an effective mass and an effective potential energy surface composed of electronic and harmonic zero-point vibrational energies of small amplitude motions in the molecule.<br>The method has been shown to work in cases of three model motions: nitrogen inversion in ammonia, single proton transfer in malonaldehyde, and double proton transfer in the formic acid dimer. In the current work we also investigate the performance of different DFT and post-Hartree-Fock methods for prediction of the proton transfer tunneling splittings, quality of the effective Schrödinger equation parameters upon the isotopic substitution, and possibility of a complete basis set (CBS) extrapolation for the resulting tunneling splittings.<br>

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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