Matrix representation of Schrödinger's Equation and its implications for the quantum mechanical inversion problem (The)

2021 ◽  
Author(s):  
Michael M. Pence
Keyword(s):  
Matrix Representation ◽  
Quantum Mechanical ◽  
Inversion Problem

scholarly journals Quantum Mechanical 4-dimensional Non-polarizing Beamsplitter

2021 ◽  
Author(s):  
Artem Kryvobok ◽  
Alan Kathman
Keyword(s):  
Quantum Computing ◽  
Scalar Field ◽  
Experimental Evidence ◽  
Vector Fields ◽  
Matrix Representation ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Simple Experiment ◽  
Canonical Commutation Relations ◽  
Classical Fields

Abstract The effects of a beamsplitter are frequently described mathematically as a matrix acting on a two input ports vector. This might be comprehensive for a scalar field but certainly insufficient in case of photons which are vector fields. In this paper we discuss theoretical grounds to define elements of a 4x4 matrix to more accurately represent the beamsplitter, fully accounting for transverse polarization modes. We also provide experimental evidence confirming this matrix representation. From scientific point of view the paper addresses a non-trivial equivalence between the classical fields Fresnel formalism and the canonical commutation relations of the quantized photonic fields. That the formalism can be readily verified with a simple experiment provides further benefit. The beamsplitter expression derived can be applied in the field of quantum computing.

scholarly journals Quantum mechanical four-dimensional non-polarizing beamsplitter

2021 ◽  
Author(s):  
Artem Kryvobok ◽  
Alan D. Kathman
Keyword(s):  
Quantum Computing ◽  
Phase Shift ◽  
Matrix Representation ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Reflection Coefficients ◽  
Classical Electromagnetism ◽  
Simple Experiment ◽  
Transverse Modes ◽  
Classical Fields

AbstractSome quantum optics researchers might not realize that classical electromagnetism predicts a $$\mathbf {\pi }$$ π phase shift between S- and P-polarized reflection and might think the reflection coefficients of the transverse modes are independent, or that such a phase shift has no measurable consequences. In this paper, we discuss theoretical grounds to define elements of a 4x4 matrix to represent the beamsplitter, accurately accounting for transverse polarization modes and phase relations between them. We also provide experimental evidence confirming this matrix representation. From a scientific point of view, the paper addresses a non-trivial equivalence between the classical fields Fresnel formalism and the canonical commutation relations of the quantized photonic fields. That the formalism can be readily verified with a simple experiment provides further benefit. The beamsplitter expression derived can be applied in the field of quantum computing.

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.

Optical and Electrical Properties of Organic Conducting Polymers

2014 ◽  
Vol 8 (1) ◽  
pp. 1457-1463
Author(s):  
Salah Abdulla Hasoon
Keyword(s):  
Electrical Properties ◽  
Conjugated Polymer ◽  
Polymeric Materials ◽  
Quantum Mechanical ◽  
Optical And Electrical Properties ◽  
Electrically Conducting ◽  
Temperature Ranges ◽  
Lithium Tetrafluoroborate ◽  
Absorbance Peak ◽  
Polymerization Method

Novel electrically conducting polymeric materials are prepared in this work. Polythiophene (PT) and poly (3-Methelthiophene) (P3MT) films were prepared by electro-polymerization method using cyclic voltammetry in acetonitrile as a solvent and lithium tetrafluoroborate as the electrolyte on a gold electrode. Electrical properties of P3MT have been examined in different environments using UV-Vis absorption spectroscopy and quantum mechanical ab initio calculations, The observed absorption peaks at 314 and 415 nm, were attributed to the n-π* and π-π* transitions, respectively in the conjugated polymer chain, in contrast, the observed absorbance peak at 649 nm, is responsible for electric conduction. The temperature dependence of the conductivity can be fitted to the Arrhenius and the VTF equations in different temperature ranges.

Bonded Force Constant Derivation of Lysine-Arginine Cross-linked Advanced Glycation End-Products

2018 ◽  
Author(s):  
Anthony Nash ◽  
Nora H de Leeuw ◽  
Helen L Birch
Keyword(s):  
Molecular Dynamics ◽  
Force Constant ◽  
Computational Study ◽  
Force Constants ◽  
Quantum Mechanical ◽  
Advanced Glycation ◽  
Partial Charges ◽  
Cross Links ◽  
Complete Set ◽  
Dynamics Simulations

<div> <div> <div> <p>The computational study of advanced glycation end-product cross- links remains largely unexplored given the limited availability of bonded force constants and equilibrium values for molecular dynamics force fields. In this article, we present the bonded force constants, atomic partial charges and equilibrium values of the arginine-lysine cross-links DOGDIC, GODIC and MODIC. The Hessian was derived from a series of <i>ab initio</i> quantum mechanical electronic structure calculations and from which a complete set of force constant and equilibrium values were generated using our publicly available software, ForceGen. Short <i>in vacuo</i> molecular dynamics simulations were performed to validate their implementation against quantum mechanical frequency calculations. </p> </div> </div> </div>

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