Creating Quantum Mechanics

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Wave Functions ◽  
Werner Heisenberg ◽  
Wolfgang Pauli ◽  
Classical Physics ◽  
Matrix Mechanics ◽  
Erwin Schrödinger ◽  
Specific Formula ◽  
The Creation

In addition to recounting some contemporary scientific history, Chapter 6 describes the hypothesis that matter, like light, can display wavelike properties, and the creation of the various formulations of quantum mechanics. That matter could have a wavelength was proposed in 1924 by Louis de Broglie, who presented a specific formula for calculating it, one that was verified experimentally in 1927. However, de Broglie’s hypothesis was overshadowed by the creation of three versions of quantum mechanics in 1925/26. The first, denoted matrix mechanics, was proposed by Werner Heisenberg. It was quickly and successfully applied by Wolfgang Pauli to the hydrogen atom. Paul Dirac introduced the next version, which was followed by that of Erwin Schrödinger via a wave equation whose solutions, denoted wave functions, were soon interpreted byMax Born to be related to the probability that certain outcomes or events will occur: classical-physics determinism was thereby removed from quantum mechanics.

scholarly journals Schrodinger Wave Equation

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Aaron C.H. Davey
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Quantum Theory ◽  
System Change ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
One Dimensional ◽  
Erwin Schrödinger ◽  
The One ◽  
Over Time

The father of quantum mechanics, Erwin Schrodinger, was one of the most important figures in the development of quantum theory. He is perhaps best known for his contribution of the wave equation, which would later result in his winning of the Nobel Prize for Physics in 1933. The Schrodinger wave equation describes the quantum mechanical behaviour of particles and explores how the Schrodinger wave functions of a system change over time. This project is concerned about exploring the one-dimensional case of the Schrodinger wave equation in a harmonic oscillator system. We will give the solutions, called eigenfunctions, of the equation that satisfy certain conditions. Furthermore, we will show that this happens only for particular values called eigenvalues.

scholarly journals A ONE-COMPONENT DIRAC EQUATION

1996 ◽  
Vol 11 (21) ◽  
pp. 3973-3985 ◽  
Author(s):  
STEFANO DE LEO
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Dirac Equation ◽  
Wave Functions ◽  
Free Wave ◽  
Quaternionic Quantum Mechanics

We develop a relativistic free wave equation on the complexified quaternions, linear in the derivatives. Even if the wave functions are only one-component, we show that four independent solutions, corresponding to those of the Dirac equation, exist. A partial set of translations between complex and complexified quaternionic quantum mechanics may be defined.

Texte zur Quantentheorie

2020 ◽  
Author(s):  
Moritz Schlick
Keyword(s):  
Werner Heisenberg ◽  
Max Planck ◽  
Wolfgang Pauli ◽  
Hans Reichenbach ◽  
Max Born ◽  
Erwin Schrödinger

Die in diesem Band zusammengestellten Texte Schlicks aus den Zwanziger- und Dreißigerjahren vermitteln vor dem Hintergrund der Einstein’schen Relativitätsrevolution das Bild einer Zeit des radikalen Umbruchs und der Entstehung des Neuen in der Physik. Als Protagonist einer Epoche intensiver Wechselwirkung zwischen naturwissenschaftlicher Forschung und philosophischer Reflexion stand Schlick, der bei Max Planck promoviert wurde, in einem intensiven Gedankenaustausch mit der Gemeinschaft der Quantenphysiker, wozu u. a. Max Born, Werner Heisenberg, Erwin Schrödinger, Pascual Jordan und Wolfgang Pauli zählten. Während sie der noch jungen Theorie der Quanten zum Durchbruch verhalfen, lieferte Schlick vor allem in Auseinandersetzung mit Hans Reichenbach und unter dem Einfluss der sprachphilosophischen Wende Ludwig Wittgensteins stehend zentrale Beiträge zum neuen Verständnis der physikalischen Realität, zu den Begriffen von Kausalität und Wahrscheinlichkeit, aber auch zum Problem der Messung und zum Verhältnis zwischen Physik und Biologie.

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.

Fundamentals of Quantum Mechanics

2020 ◽  
pp. 73-80
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Quantum Mechanics ◽  
Formal Theory ◽  
Uncertainty Relations ◽  
Quantum Superposition ◽  
Conceptual Foundation ◽  
Classical Physics ◽  
Max Born ◽  
Erwin Schrödinger ◽  
Heisenberg Uncertainty ◽  
Probabilistic Nature

The laws of quantum mechanics were formulated in the year 1925 through the work of Werner Heisenberg, followed by Max Born, Pascual Jordan, Paul Dirac, and Wolfgang Pauli. A separate but equivalent approach was independently developed by Erwin Schrödinger in early 1926. The laws governing quantum mechanics were highly mathematical and their aim was to explain many unresolved problems within the framework of a formal theory. The conceptual foundation emerged in the subsequent 2–3 years that indicated how radically different the new laws were from classical physics. In this chapter some of these salient features of quantum mechanics are discussed. The topics include the quantization of energy, wave–particle duality, the probabilistic nature of quantum mechanics, Heisenberg uncertainty relations, Bohr’s principle of complementarity, and quantum superposition and entanglement. This discussion should indicate how different and counterintuitive its fundamentals are from those of classical physics.

4. Enthusiastic resignation

2020 ◽  
pp. 64-83
Author(s):  
J. L. Heilbron
Keyword(s):  
Uncertainty Principle ◽  
Correspondence Principle ◽  
Spectral Lines ◽  
Werner Heisenberg ◽  
Wolfgang Pauli ◽  
Mathematical Solution ◽  
Erwin Schrödinger ◽  
Symbolic Value ◽  
Atomic Electrons

‘Enthusiastic resignation’ describes Bohr’s work with Wolfgang Pauli and Werner Heisenberg. ‘Resignation’ refers to their realization that the electron orbits that had served as the basis of Bohr’s theory had only ‘symbolic’ value. They took the correspondence principle as a guide to translating symbols describing the orbits, like position and momentum, into symbols specifying the values of observable products of atoms, like the frequency and intensity of spectral lines. Heisenberg’s breakthrough in the summer of 1925, based on a particulate view of matter, provided a basis for a coherent description of the phenomena to which atomic electrons give rise. Almost simultaneously, Erwin Schrödinger found another route to the same mathematical solution, based on a wave picture of matter, which avoided discontinuity and made calculations easier. In answering Schrödinger’s challenge, Heisenberg invented the Uncertainty Principle and Bohr worked out a more general reconciliation of the quantum puzzles, which he called ‘complementarity’.

scholarly journals Is Schrödinger's Cat Alive?

Quanta ◽  
2017 ◽  
Vol 6 (1) ◽  
pp. 70 ◽  
Author(s):  
Mani L. Bhaumik
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Equation Of Motion ◽  
Copenhagen Interpretation ◽  
Interpretation Of Quantum Mechanics ◽  
Erwin Schrödinger ◽  
Quantum Reality

Erwin Schrödinger is famous for presenting his wave equation of motion that jump-started quantum mechanics. His disenchantment with the Copenhagen interpretation of quantum mechanics led him to unveil the Schrödinger's cat paradox, which did not get much attention for nearly half a century. In the meantime, disappointment with quantum mechanics turned his interest to biology facilitating, albeit in a peripheral way, the revelation of the structure of DNA. Interest in Schrödinger's cat has recently come roaring back making its appearance conspicuously in numerous scientific articles. From the arguments presented here, it would appear that the legendary Schrödinger's cat is here to stay, symbolizing a profound truth that quantum reality exists at all scales; but we do not observe it in our daily macroscopic world as it is masked for all practical purposes, most likely by environmental decoherence with irreversible thermal effects.Quanta 2017; 6: 70–80.

scholarly journals Erwin Schrödinger and Quantum Wave Mechanics

Quanta ◽  
2017 ◽  
Vol 6 (1) ◽  
pp. 48 ◽  
Author(s):  
John J. O'Connor ◽  
Edmund F. Robertson
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Quantum Probability ◽  
Wave Mechanics ◽  
Space And Time ◽  
Erwin Schrödinger ◽  
Quantum Particles ◽  
Quantum Wave ◽  
The Veil ◽  
Matrix Quantum

<p>The fathers of matrix quantum mechanics believed that the quantum particles are <em>unanschaulich</em> (unvisualizable) and that quantum particles pop into existence only when we measure them. Challenging the orthodoxy, in 1926 Erwin Schrödinger developed his wave equation that describes the quantum particles as a packet of quantum probability amplitudes evolving in space and time. Thus, Schrödinger visualized the unvisualizable and lifted the veil that has been obscuring the wonders of the quantum world.</p><p>Quanta 2017; 6: 48–52.</p>

scholarly journals The “noncausal causality” of quantum information

2021 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Wave Functions ◽  
Probability Density Distribution ◽  
Information Function ◽  
Classical Physics ◽  
Physical Description ◽  
Probabilistic Causality ◽  
Random Probability

The paper is concentrated on the special changes of the conception of causalityfrom quantum mechanics to quantum information meaning as a background the revolution implemented by the former to classical physics and science after Max Born’s probabilistic reinterpretation of wave function. Those changes can be enumerated so: (1) quantum information describes the general case of the relation of two wave functions, and particularly, the causal amendment of a single one; (2) it keeps the physical description to be causal by the conservation of quantum information and in accordance with Born’s interpretation; (3) it introduces inverse causality, “backwards in time”, observable “forwards in time” as the fundamentally random probability density distribution of all possible measurements of any physical quantity in quantum mechanics; (4) it involves a kind of “bidirectional causality” unifying (4.1) the classical determinism of cause and effect, (4.2) the probabilistic causality of quantum mechanics, and (4.3) the reversibility of any coherent state; (5) it identifies determinism with the function successor in Peano arithmetic, and its proper generalized causality with the information function successor in Hilbert arithmetic.

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