Complex Wave Function Reconstruction and Direct Electromagnetic Field Determination from Time-Resolved Intensity Data

2012 ◽  
Vol 3 (22) ◽  
pp. 3353-3359 ◽  
Author(s):  
Cian Menzel-Jones ◽  
Moshe Shapiro
Keyword(s):  
Wave Function ◽  
Electromagnetic Field ◽  
Intensity Data ◽  
Time Resolved ◽  
Complex Wave ◽  
Function Reconstruction

scholarly journals Quaternionic wave function

2019 ◽  
Vol 34 (02) ◽  
pp. 1950001 ◽  
Author(s):  
Pavel A. Bolokhov
Keyword(s):  
Wave Function ◽  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Variational Calculus ◽  
Nonrelativistic Limit ◽  
Natural Choice ◽  
Complex Wave ◽  
Spinor Formalism ◽  
Function Language

We argue that quaternions form a natural language for the description of quantum-mechanical wave functions with spin. We use the quaternionic spinor formalism which is in one-to-one correspondence with the usual spinor language. No unphysical degrees of freedom are admitted, in contrast to the majority of literature on quaternions. In this paper, we first build a Dirac Lagrangian in the quaternionic form, derive the Dirac equation and take the nonrelativistic limit to find the Schrödinger’s equation. We show that the quaternionic formalism is a natural choice to start with, while in the transition to the noninteracting nonrelativistic limit, the quaternionic description effectively reduces to the regular complex wave function language. We provide an easy-to-use grammar for switching between the ordinary spinor language and the description in terms of quaternions. As an illustration of the broader range of the formalism, we also derive the Maxwell’s equation from the quaternionic Lagrangian of Quantum Electrodynamics. In order to derive the equations of motion, we develop the variational calculus appropriate for this formalism.

scholarly journals The Quaternionic Commutator Bracket and Its Implications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 513 ◽  
Author(s):  
Arbab Arbab ◽  
Mudhahir Al Ajmi
Keyword(s):  
Wave Function ◽  
Electromagnetic Field ◽  
Angular Momentum ◽  
Charged Particle ◽  
Magnetic Fields ◽  
Interaction Energy ◽  
Internal Structure ◽  
Magnetic Moments ◽  
Electric And Magnetic Fields ◽  
Aharonov Bohm

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, viz. ψ ˜ = ( i c ψ 0 , ψ → ) , represents a state of a particle with orbital angular momentum, L = 3 ℏ , resulting from the internal structure of the particle. This angular momentum can be attributed to spin of the particle. The vector ψ → , points in an opposite direction of L → . When a charged particle is placed in an electromagnetic field, the interaction energy reveals that the magnetic moments interact with the electric and magnetic fields giving rise to terms similar to Aharonov–Bohm and Aharonov–Casher effects.

scholarly journals Synthesis and Characterization of a Cobalt(III) Corrole with an Sbound DMSO Ligand

2021 ◽  
Author(s):  
Nicolás I. Neuman ◽  
Arijit Singha Hazari ◽  
Julia Beerhues ◽  
Fabio Doctorovich ◽  
Santiago E. Vaillard ◽  
...  
Keyword(s):  
Wave Function ◽  
Electrochemical Properties ◽  
Spectroscopic Data ◽  
Synthesis And Characterization ◽  
Frontier Orbitals ◽  
Complex Wave

A cobalt(III) corrole complex with an apical dmso ligand is presented. Crystallographic and spectroscopic data are used to unequivocally establish the dmso(O) vs. dmso(S) coordination in this complex. Wave function based methods were used to calculate the frontier orbitals for the complexes with O-bound and S-bound dmso ligands. Electrochemical properties of the complex is presented as well.<br>

scholarly journals A novel view on successive quantizations, leading to increasingly more “miraculous” states

2019 ◽  
Vol 34 (23) ◽  
pp. 1950186 ◽  
Author(s):  
Matej Pavšič
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Function ◽  
Wave Packet ◽  
Time Derivative ◽  
Point Particle ◽  
Order Equation ◽  
Quantum Field ◽  
First Order ◽  
Complex Wave

A series of successive quantizations is considered, starting with the quantization of a non-relativistic or relativistic point particle: (1) quantization of a particle’s position, (2) quantization of wave function, (3) quantization of wave functional. The latter step implies that the wave packet profiles forming the states of quantum field theory are themselves quantized, which gives new physical states that are configurations of configurations. In the procedure of quantization, instead of the Schrödinger first-order equation in time derivative for complex wave function (or functional), the equivalent second-order equation for its real part was used. In such a way, at each level of quantization, the equation a quantum state satisfies is just like that of a harmonic oscillator, and wave function(al) is composed in terms of the pair of its canonically conjugated variables.

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