scholarly journals Application of Einstein’s Methods in a Quantum Theory of Radiation

2021 ◽  
Author(s):  
Richard Joseph Oldani
Keyword(s):  
Theoretical Models ◽  
Lagrangian Model ◽  
Quantum Mechanical ◽  
Quantum Oscillator ◽  
Wave Mechanics ◽  
Momentum Exchange ◽  
Dynamical Equilibrium ◽  
Matrix Mechanics ◽  
Quantum Theory Of Radiation ◽  
Electron Photon

Einstein showed in his seminal paper on radiation that molecules with a quantum-theoretical distribution of states in thermal equilibrium are in dynamical equilibrium with the Planck radiation. The method he used assigns coordinates fixed with respect to molecules to derive the A and B coefficients, and fixed relative to laboratory coordinates to specify their thermal motion. The resulting dynamical equilibrium between quantum mechanical and classically defined statistics is critically dependent upon considerations of momentum exchange. When Einstein’s methods relating classical and quantum mechanical statistical laws are applied to the level of the single quantum oscillator they show that matrix mechanics describes the external appearances of an atom as determined by photon-electron interactions in laboratory coordinates, and wave mechanics describes an atom’s internal structure according to the Schrödinger wave equation. Non-commutation is due to the irreversibility of momentum exchange when transforming between atomic and laboratory coordinates. This allows the “rotation” of the wave function to be interpreted as the changing phase of an electromagnetic wave. In order to describe the momentum exchange of a quantum oscillator the Hamiltonian model of atomic structure is replaced by a Lagrangian model that is formulated with equal contributions from electron, photon, and nucleus. The fields of the particles superpose linearly, but otherwise their physical integrity is maintained throughout. The failure of past and present theoretical models to include momentum is attributed to the overwhelming requirement of human visual systems for an explicit stimulus.

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.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

The quantum mechanical theory of environmental effects

1960 ◽  
Vol 255 (1280) ◽  
pp. 63-68 ◽  
Keyword(s):  
Wave Function ◽  
Environmental Effects ◽  
Quantum Mechanical ◽  
Mechanical Theory ◽  
Wave Mechanics ◽  
Quantum Mechanical Theory ◽  
The Individual

A basic postulate of wave mechanics is that the wave function of a microscopic system develops in time according to the equation iℏ∂ψ/∂ t = H ψ, where H , the Hamiltonian, is an operator which in general depends upon the time. If, and only if, the Hamiltonian is time-independent, then the solutions of this equation take the form ψ( q, t ) = ∑ n c n Ѱ n ( q )e -1 E n t /ℏ , (2) where the individual terms Ѱ n ( q ) are functions of the co-ordinates alone and the E n are the corresponding eigenvalues of the Hamiltonian, satisfying HѰ n = E n Ѱ n . (3)

Molecular X-ray Spectra of Sulfur and Chlorine Bearing Substances

1970 ◽  
Vol 14 ◽  
pp. 453-486 ◽  
Author(s):  
G. Andermann ◽  
H. C. Whitehead
Keyword(s):  
Theoretical Models ◽  
Quantum Mechanical ◽  
Quantum Mechanical Calculations ◽  
Molecular Models ◽  
X Ray ◽  
Starting Point ◽  
State Models ◽  
Basic Features ◽  
Photon Spectra ◽  
Molecular Bonding

AbstractThe interpretation and use of x-ray photon spectra of substances containing second row elements has utilized a number of theoretical models. These models may be divided into three basic categories, namely, the isolated atom model, various molecular models, and a number of solid state models, it is the purpose of this paper to examine critically the validity and limitations of molecular models for interpreting published x-ray photon spectra and spectra obtained by this group on chlorine and sulfur bearing substances.Chlorine and sulfur bearing substances were chosen for at least three important reasons. First, a great deal of published experimental data already exists on the Kα, Kβ, and L2, 3 transitions of these substances. Second, motivated in part by the long standing controversy concerning possible 3d orbital participation in the bonding of second row elements, there are extensive quantum mechanical calculations for ions containing sulfur and chlorine via simple molecular orbital concepts. Thirdj the availability of accurate photoelectron spectroscopic data on these substances now permits a detailed quantitative comparison of x-ray photon transitions with quantum mechanical calculations.Detailed evaluation along these lines indicates that for many substances the theoretically calculated energy values are frequently within a few electron volts (or less) of the experimentally observed energies. This study, therefore, tends to substantiate a viewpoint suggested by some recently; namely, that for many substances the starting point in interpreting most of the basic features of soft x-ray spectra should be based upon molecular bonding approaches.

scholarly journals Lorentz Atom Revisited by Solving the Abraham–Lorentz Equation of Motion

2017 ◽  
Vol 72 (8) ◽  
pp. 717-731 ◽  
Author(s):  
Jürgen Bosse
Keyword(s):  
Steady State Solution ◽  
Equation Of Motion ◽  
Photon Absorption ◽  
Forced Oscillations ◽  
Quantum Mechanical ◽  
Quantum Oscillator ◽  
Great Success ◽  
Deep Insight ◽  
Lorentz Equation ◽  
Insight Into

AbstractBy solving the non-relativistic Abraham–Lorentz (AL) equation, I demonstrate that the AL equation of motion is not suited for treating the Lorentz atom, because a steady-state solution does not exist. The AL equation serves as a tool, however, for deducing the appropriate parameters Ω and Γ to be used with the equation of forced oscillations in modelling the Lorentz atom. The electric polarisability, which many authors “derived” from the AL equation in recent years, is shown to violate Kramers–Kronig relations rendering obsolete the extracted photon-absorption rate, for example. Fortunately, errors turn out to be small quantitatively, as long as the light frequency ω is neither too close to nor too far from the resonance frequency Ω. The polarisability and absorption cross section are derived for the Lorentz atom by purely classical reasoning and are shown to agree with the quantum mechanical calculations of the same quantities. In particular, oscillator parameters Ω and Γ deduced by treating the atom as a quantum oscillator are found to be equivalent to those derived from the classical AL equation. The instructive comparison provides a deep insight into understanding the great success of Lorentz’s model that was suggested long before the advent of quantum theory.

Quantum Physics

2017 ◽  
Author(s):  
Suman Seth
Keyword(s):  
Quantum Physics ◽  
Subsequent Development ◽  
Atomic Spectroscopy ◽  
Irreversible Processes ◽  
Wave Mechanics ◽  
Matrix Mechanics ◽  
Max Born ◽  
History Of ◽  
Post War ◽  
History Of Quantum Physics

This article discusses the history of quantum physics, beginning with an analysis of the process through which a community of quantum theorists and experimentalists came into being. In particular, it traces the roots and fruits of Max Planck’s papers in irreversible processes in nature. It proceeds by exploring the origin and subsequent development of Niels Bohr’s so-called ‘planetary model’ of the atom, focusing on the extension of the model by Arnold Sommerfeld and members of his school as well to Bohr’s use of his principles of correspondence and adiabatic invariance. It also considers the post-war years, as the problems of atomic spectroscopy sparked the development of new methodological approaches to quantum theory. Finally, it offers a history of the two distinct new forms of quantum mechanics put forward in the mid-1920s: Werner Heisenberg, Max Born, and Pascual Jordan’s matrix mechanics, and Erwin Schrödinger’s wave mechanics.

Oppenheimer's first paper: Molecular band spectra and a professional style

2007 ◽  
Vol 37 (2) ◽  
pp. 247-270 ◽  
Author(s):  
David C. Cassidy
Keyword(s):  
Quantum Mechanics ◽  
20Th Century ◽  
Spectral Lines ◽  
Molecular Band ◽  
Wave Mechanics ◽  
Infrared Band ◽  
Commutator Algebra ◽  
Matrix Mechanics ◽  
Characteristic Features ◽  
Band Spectra

Beginning early in the 20th century spectroscopists attributed the infrared band spectra emitted by diatomic molecules to quantum vibration and rotation modes of the molecules. Because of these relatively simple motions, band spectra offered a convenient .rst phenomenon to which to apply formulations of the new quan-tum mechanics in 1926. In his .rst paper, completed in Cambridge in May 1926, Oppenheimer presented a derivation of the frequencies and relative intensities of the observed spectral lines on the basis of Paul Dirac's new quantum commutator algebra. At the same time Lucy Mensing published a similar derivation utiliz-ing matrix mechanics, as did Edwin Fues utilizing wave mechanics. Analyses of Oppenheimer's paper and of its historical and scienti.c contexts offer insights into the new quantum mechanics and its utilization and reception during this brief period of competing formalisms, and into the characteristic features of Oppenheimer's later style of research and publication.

Theoretical Models of Schottky Barriers

1981 ◽  
Vol 10 ◽  
Author(s):  
M. Schluter
Keyword(s):  
Theoretical Models ◽  
Interface States ◽  
Schottky Barriers ◽  
Quantum Mechanical ◽  
Barrier Heights

ABSTRACTA review is presented in which existing theories of the formation of Schottky barriers are analyzed. The list includes macroscopic dielectric approaches and various microscopic quantum mechanical treatments. The central role of interface states and their different physical origins are assessed. Simple concepts, able to predict general trends in barrier heights, are examined along with detailed microscopic theories applied to individual contacts.

Visualizability and Intelligibility

2017 ◽  
Author(s):  
Henk W. de Regt
Keyword(s):  
Quantum Physics ◽  
Niels Bohr ◽  
Wave Mechanics ◽  
Classical Physics ◽  
Matrix Mechanics ◽  
Contextual Theory ◽  
Erwin Schrödinger ◽  
Gradual Loss ◽  
Depth Study

This chapter investigates the relation between visualizability and intelligibility, by means of an in-depth study of the transition from classical physics to quantum physics in the first decades of the twentieth century. In this development, the issue of visualizability played a central role. After a brief discussion of the visualizability of classical physics, it examines the gradual loss of visualizability in quantum theory, focusing on the work of quantum physicists Niels Bohr, Wolfgang Pauli, Werner Heisenberg, and Erwin Schrödinger. The chapter presents a detailed analysis of the role of visualizability (Anschaulichkeit) in the competition between Schrödinger’s wave mechanics and Heisenberg’s matrix mechanics, and in the discovery of electron spin. The contextual theory of understanding asserts that visualizability is one out of many possible tools for understanding, albeit one that has proved to be very effective in science. This conclusion is supported by an analysis of the role of visualization in postwar quantum physics, especially via Feynman diagrams.

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