scholarly journals Quantum mechanical calculation of electron spin

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 652-661
Author(s):  
Hai-Long Zhao
Keyword(s):  
Wave Function ◽  
Electron Spin ◽  
Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Classical Method ◽  
Boltzmann Distribution ◽  
Quantum Mechanical ◽  
Rest Energy ◽  
Self Energy ◽  
Mechanical Methods

AbstractThe classical and quantum mechanical methods are used respectively to calculate the electron spin. It is shown that the classical method cannot derive the correct magnetic moment value. Assuming that the rest energy of the electron originates from the kinetic energy of the virtual particles, the electron spin motion equation and spin wave function can be derived. In the case of the quantum numbers of spin angular momentum and magnetic moment being 1/2 and 1 respectively, their correct values can be obtained. In the meanwhile, the anomalous magnetic moment is evaluated based on the wave function of the spinning electron. Suppose the probability of virtual photons converting into electron-positron pairs to be 0.00141, the result agrees with that of quantum electrodynamics. Given that the energy of the virtual photon obeys the classical Maxwell-Boltzmann distribution, the self-energy of the electron will be finite. In addition, the hierarchy problem can be solved with the same hypothesis.

scholarly journals Quantum electrodynamics with self-conjugated equations with spinor wave functions for fermion fields

2021 ◽  
pp. 2150086
Author(s):  
V. P. Neznamov ◽  
V. E. Shemarulin
Keyword(s):  
Cross Sections ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Wave Functions ◽  
Self Energy ◽  
Fermion Fields ◽  
Spinor Wave

Quantum electrodynamics (QED) with self-conjugated equations with spinor wave functions for fermion fields is considered. In the low order of the perturbation theory, matrix elements of some of QED physical processes are calculated. The final results coincide with cross-sections calculated in the standard QED. The self-energy of an electron and amplitudes of processes associated with determination of the anomalous magnetic moment of an electron and Lamb shift are calculated. These results agree with the results in the standard QED. Distinctive feature of the developed theory is the fact that only states with positive energies are present in the intermediate virtual states in the calculations of the electron self-energy, anomalous magnetic moment of an electron and Lamb shift. Besides, in equations, masses of particles and antiparticles have the opposite signs.

scholarly journals Big picture of relativistic molecular quantum mechanics

2015 ◽  
Vol 3 (2) ◽  
pp. 204-221 ◽  
Author(s):  
Wenjian Liu
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Electrodynamics ◽  
Relativistic Quantum ◽  
Coupling Constants ◽  
Quantum Mechanical ◽  
Big Picture ◽  
The Right ◽  
Molecular Quantum Mechanics ◽  
Energy Property

Abstract Any quantum mechanical calculation on electronic structure ought to choose first an appropriate Hamiltonian H and then an Ansatz for parameterizing the wave function Ψ, from which the desired energy/property E(λ) can finally be calculated. Therefore, the very first question is: what is the most accurate many-electron Hamiltonian H? It is shown that such a Hamiltonian i.e. effective quantum electrodynamics (eQED) Hamiltonian, can be obtained naturally by incorporating properly the charge conjugation symmetry when normal ordering the second quantized fermion operators. Taking this eQED Hamiltonian as the basis, various approximate relativistic many-electron Hamiltonians can be obtained based entirely on physical arguments. All these Hamiltonians together form a complete and continuous ‘Hamiltonian ladder’, from which one can pick up the right one according to the target physics and accuracy. As for the many-electron wave function Ψ, the most intriguing questions are as follows. (i) How to do relativistic explicit correlation? (ii) How to handle strong correlation? Both general principles and practical strategies are outlined here to handle these issues. Among the electronic properties E(λ) that sample the electronic wave function nearby the nuclear region, nuclear magnetic resonance (NMR) shielding and nuclear spin-rotation (NSR) coupling constant are especially challenging: they require body-fixed molecular Hamiltonians that treat both the electrons and nuclei as relativistic quantum particles. Nevertheless, they have been formulated rigorously. In particular, a very robust ‘relativistic mapping’ between the two properties has been established, which can translate experimentally measured NSR coupling constants to very accurate absolute NMR shielding scales that otherwise cannot be obtained experimentally. Since the most general and fundamental issues pertinent to all the three components of the quantum mechanical equation HΨ = EΨ (i.e. Hamiltonian H, wave function Ψ, and energy/property E(λ)) have fully been understood, the big picture of relativistic molecular quantum mechanics can now be regarded as established.

The Electron Self-Energy in a Classical Spin Model

1997 ◽  
Vol 11 (05) ◽  
pp. 189-193
Author(s):  
J. Frenkel ◽  
R. B. Santos
Keyword(s):  
Simple Model ◽  
Electric Charge ◽  
Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Spin Model ◽  
G Factor ◽  
Linear Speed ◽  
Classical Spin ◽  
Self Energy ◽  
Spinning Disk

We discuss a simple model where the electron is approximately described by a rapidly spinning disk of radius λ=ℏ/mc, such that the linear speed at its border is c. We assume that the particle's mass is uniformly distributed over the surface of the disk and its electric charge is strongly peaked around the border. It follows that the spin of the particle must be ℏ/2 and its magnetic moment should have a g factor equal to 2. We show that the electromagnetic self-energy of the particle is given by an expression which is similar to the result obtained in quantum electrodynamics.

Operators and meaning of wave function

2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
State Vector ◽  
The State ◽  
Physical Significance ◽  
Central Problem ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Interpretation Of Quantum Theory

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

scholarly journals Interactions between large molecules pose a puzzle for reference quantum mechanical methods

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yasmine S. Al-Hamdani ◽  
Péter R. Nagy ◽  
Andrea Zen ◽  
Dennis Barton ◽  
Mihály Kállay ◽  
...  
Keyword(s):  
Experimental Information ◽  
Quantum Mechanical ◽  
Interaction Energies ◽  
Small Organic Molecules ◽  
Large Molecules ◽  
Reference Information ◽  
Mechanical Methods ◽  
Non Covalent Interactions ◽  
Semi Empirical ◽  
Covalent Interactions

AbstractQuantum-mechanical methods are used for understanding molecular interactions throughout the natural sciences. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] are state-of-the-art trusted wavefunction methods that have been shown to yield accurate interaction energies for small organic molecules. These methods provide valuable reference information for widely-used semi-empirical and machine learning potentials, especially where experimental information is scarce. However, agreement for systems beyond small molecules is a crucial remaining milestone for cementing the benchmark accuracy of these methods. We show that CCSD(T) and DMC interaction energies are not consistent for a set of polarizable supramolecules. Whilst there is agreement for some of the complexes, in a few key systems disagreements of up to 8 kcal mol−1 remain. These findings thus indicate that more caution is required when aiming at reproducible non-covalent interactions between extended molecules.

scholarly journals A Review on Combination of Ab Initio Molecular Dynamics and NMR Parameters Calculations

2021 ◽  
Vol 22 (9) ◽  
pp. 4378
Author(s):  
Anna Helena Mazurek ◽  
Łukasz Szeleszczuk ◽  
Dariusz Maciej Pisklak
Keyword(s):  
Molecular Dynamics ◽  
Ab Initio ◽  
Small Amplitude ◽  
Ab Initio Molecular Dynamics ◽  
Quantum Mechanical ◽  
Time Step ◽  
Noticeable Effect ◽  
Nmr Parameters ◽  
Mechanical Methods ◽  
Simulation Time

This review focuses on a combination of ab initio molecular dynamics (aiMD) and NMR parameters calculations using quantum mechanical methods. The advantages of such an approach in comparison to the commonly applied computations for the structures optimized at 0 K are presented. This article was designed as a convenient overview of the applied parameters such as the aiMD type, DFT functional, time step, or total simulation time, as well as examples of previously studied systems. From the analysis of the published works describing the applications of such combinations, it was concluded that including fast, small-amplitude motions through aiMD has a noticeable effect on the accuracy of NMR parameters calculations.

scholarly journals New Approach for Correcting Noncovalent Interactions in Semiempirical Quantum Mechanical Methods: The Importance of Multiple-Orientation Sampling

2021 ◽  
Vol 17 (9) ◽  
pp. 5556-5567
Author(s):  
Sergio Pérez-Tabero ◽  
Berta Fernández ◽  
Enrique M. Cabaleiro-Lago ◽  
Emilio Martínez-Núñez ◽  
Saulo A. Vázquez
Keyword(s):  
Noncovalent Interactions ◽  
Quantum Mechanical ◽  
New Approach ◽  
Mechanical Methods

scholarly journals Macroscopic Virtual Particles Exist

2019 ◽  
Vol 74 (5) ◽  
pp. 363-366
Author(s):  
Günter Nimtz
Keyword(s):  
Quantum Electrodynamics ◽  
Quantum Mechanical ◽  
Wave Mechanics ◽  
Virtual Particles

AbstractVirtual particles are expected to occur in microscopic processes, as they are introduced, for instance, by Feynman in quantum electrodynamics as photons performing in an unknown way in the interaction between two electrons. This note describes macroscopic virtual particles as they appear in classical evanescent modes and in quantum mechanical tunnelling particles. Remarkably, these large virtual particles are present in wave mechanics of elastic, electromagnetic, and Schrödinger fields.

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