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.

scholarly journals Quantum gravity as the unification of general relativity and quantum mechanics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Wave Mechanics ◽  
Matrix Mechanics ◽  
System P

nonstandard viewpoint to quantum gravity is discussed. General relativity and quantum mechanics are to be related as two descriptions of the same, e.g. as Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics merged in the contemporary quantum mechanics. From the viewpoint of general relativity one can search for that generalization of relativity implying the invariance “within – out of” of the same system.

scholarly journals The physical interpretation of the quantum dynamics

1927 ◽  
Vol 113 (765) ◽  
pp. 621-641 ◽  
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Dynamics ◽  
Energy Levels ◽  
Classical Mechanics ◽  
Incident Radiation ◽  
Spectral Lines ◽  
Original Matrix ◽  
Matrix Mechanics ◽  
The Matrix

The new quantum mechanics consists of a scheme of equations which are very closely analogous to the equations of classical mechanics, with the funda­mental difference that the dynamical variables do not obey the commutative law of multiplication, but satisfy instead the well-known quantum conditions. It follows that one cannot suppose the dynamical variables to be ordinary numbers (c-numbers), but may call them numbers of a special type (q-numbers). The theory shows that these q-numbers can in general be represented by matrices whose elements are c-numbers (functions of a time parameter). When one has performed the calculations with the q-numbers and obtained all the matrices one wants, the question arises how one is to get physical results from the theory, i. e., how can one obtain c-numbers from the theory that one can compare with experimental values ? Hitherto this has been done with the help of a number of special assumptions. In Heisenberg’s original matrix mechanics it was assumed that the elements of the diagonal matrix that repre­sents the energy are the energy levels of the system, and the elements of the matrix that represents the total polarisation, which are periodic functions of the time, determine the frequencies and intensities of the spectral lines in analogy to the classical theory. Schrodinger’s wave representation of the quantum mechanics has provided new ways of obtaining physical results from the theory, based on the assumption that the square of the amplitude of the wave function can in certain cases be interpreted as a probability. From this assumption one can, for instance, work out the probability of a transition being produced in a system (or the number of transitions produced in an assembly of like systems) by an arbitrary external perturbing force, and can thus, by supposing the perturbation to consist of incident radiation, obtain directly Einstein’s B coefficients. Again in Born’s treatment of collision problems it is assumed that the square of the amplitude of the wave function scattered in any direction determines the probability of the colliding electron (or other body) being scattered in that direction.

An Exercise in a Transdisciplinary Approach for New Knowledge Paradigms

2014 ◽  
Vol 3 (3) ◽  
pp. 114-143
Author(s):  
Gabriel Crumpei ◽  
Maricel Agop ◽  
Alina Gavriluţ ◽  
Irina Crumpei
Keyword(s):  
Quantum Mechanics ◽  
20Th Century ◽  
Chaos Theory ◽  
Fractal Geometry ◽  
Science And Religion ◽  
Transdisciplinary Approach ◽  
Linear Dynamics ◽  
New Knowledge ◽  
Religious Perspectives ◽  
Energy Information

Abstract In this paper, we aim at an exercise that is transdisciplinary, involving science and religion, and interdisciplinary, involving disciplines and theories which appeared in the second half of the 20th century (e.g., topology, chaos theory, fractal geometry, non-linear dynamics, all of which can be found in the theory of complex systems). The latter required the reformulation of quantum mechanics theories starting with the beginning of the century, based on the substance-energy-information triangle. We focus on information and we also attempt a transdisciplinary approach to the imaginary from a psychological - physical - mathematical perspective, but the religious perspectives find their place along with the philosophical or even philological vision

Constructing Quantum Mechanics

2019 ◽  
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Black Body ◽  
Black Body Radiation ◽  
Wave Mechanics ◽  
Specific Heats ◽  
Old Quantum Theory ◽  
Upper Level

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.

scholarly journals Revolutions in the earth sciences

1999 ◽  
Vol 354 (1392) ◽  
pp. 1915-1919 ◽  
Author(s):  
Claude Allègre ◽  
Vincent Courtillot
Keyword(s):  
Earth Sciences ◽  
Quantum Mechanics ◽  
20Th Century ◽  
Plate Tectonics ◽  
Statistical Physics ◽  
Natural Sciences ◽  
Scientific Revolutions ◽  
The Earth

The 20th century has been a century of scientific revolutions for many disciplines: quantum mechanics in physics, the atomic approach in chemistry, the nonlinear revolution in mathematics, the introduction of statistical physics. The major breakthroughs in these disciplines had all occurred by about 1930. In contrast, the revolutions in the so–called natural sciences, that is in the earth sciences and in biology, waited until the last half of the century. These revolutions were indeed late, but they were no less deep and drastic, and they occurred quite suddenly. Actually, one can say that not one but three revolutions occurred in the earth sciences: in plate tectonics, planetology and the environment. They occurred essentially independently from each other, but as time passed, their effects developed, amplified and started interacting. These effects continue strongly to this day.

Historical and logical analysis of research on the development of professional value orientations of students in the context of Internet socialization

2020 ◽  
pp. 7-14
Author(s):  
Marina S. Chvanova ◽  
Irina A. Kiselyova
Keyword(s):  
Young People ◽  
20Th Century ◽  
Value Orientations ◽  
Logical Analysis ◽  
Early 20Th Century ◽  
Logical Sequence ◽  
Characteristic Features ◽  
Over Time ◽  
Professional Value

We examine the formation of the concept of “value orientations”, “professional value orientations of students”. The classification is presented taking into account the following profes-sional value orientations: “professional and personal”, “professional and group”, “social and pro-fessional”. Professional value orientations are analyzed taking into account their importance, with subdivision into instrumental and terminal ones. We consider the development of professional value orientations in a historical and logical sequence with a change of stages, with characteristic features, taking into account the presented classification. The following periods are considered: the second half of the 19th – early 20th century, 20–40s of the 20th century, 50–60s of the 20th century, 60–80s of the 20th century, 80–90s of the 20th century, 21th century. The characteristic features of the stage, the means of influencing the value orientations of young people, are analyzed, which made it possible to identify the transformation of professional value orientations over time, including in the context of Internet socialization.

scholarly journals Research of the History of Inter-Religious Relations in Ukraine in the Kyiv Theological Academy (Second Half of the 19th – Beginning of the 20th Century)

2021 ◽  
Vol 8 ◽  
pp. 60-79
Author(s):  
Luidmila Pastushenko
Keyword(s):  
20Th Century ◽  
19Th Century ◽  
Legal Aspects ◽  
Systematic Analysis ◽  
Literary Traditions ◽  
The Social ◽  
Academic Researchers ◽  
History Of ◽  
Characteristic Features ◽  
The 19Th Century

The article presents the first attempt of a complete and systematic analysis of historic and theological publications of teachers and pupils of the Kyiv Theological Academy in the second half of the 19th – beginning of 20th century in the field of studying the history of relations of Catholicism and Protestantism with Orthodox on the Ukrainian lands. The specifics of Kyiv academic historians studies was determined by the social and-political circumstances in the middle of the 19th century and denoted by an attempt to comprehend this issue in the perspective of the history of interconfessional relations of two Western Christian traditions with the eastern tradition of Orthodoxy in the historical gap of the 16th – 17th centuries – the period of the largest confrontation in confessional relations in Ukraine. The author clarifies the characteristic features of researching the question of inter-confessional interaction in the 15th – 17th centuries, which are expressed in attempts to describe the coexistence of three denominations as multidimensional and provoking а variety of different interpretations. Historical studies present the attempt to show confessional interaction in the political and legal aspects and to provide historical interpretations to the ground of philosophy of history. The article proves the tendency of Kyiv academic researchers to move away from the established Russian historiography of the 19th century view at confessional relations in Ukraine through the prism of hard confrontation and outline in religious life Ukraine conditions and circumstances of inter-confessional dialogue. Also, historians in their studies repeatedly note the significant educational and outlook influence of Western Christian denominations on the formation of educational, cultural, theological, literary traditions in Ukraine.

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.

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