Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Chemical Education

Wave mechanics without waves

S. M. Blinder

Published Aug 1, 1974• 0 citations
Publisher

Abstract

This article describes an approach to describing wave mechanics that is less mathematically intense than currently popular approaches.
DOI
10.1021/ed051p515

Related papers

The Formulation of Wave Mechanics

Alessandro Teta

UNITEXT for physics•Jan 1, 2018•0 citations

The electron as a vector wave

C. G. DARWIN

Abstract In an article in ‘Nature’ last February I put forward a suggestion, of necessity in so concise a form as to be not very easily intelligible, that when the magnetic properties of the atom are regarded from the point of view of the wave mechanics, they suggest that the electron is to be taken as a wave of two components, like light, not of one like sound. The theory and its mathematical development were only outlined in ‘Nature,’ and the object of the present work is to give them in fuller detail. Recently Pauli has published a paper on the same subject, and arrived at the same mathematical results, but owing to the fact that he is more disposed to regard the wave theory as a mathematical convenience and less as a physical reality, he stops short of the point which was the guiding principle to me, and refuses to interpret the two functions that we both obtain as formed from a vector. I shall therefore here develop somewhat fully the arguments and analogies which seem to me to show that the vector is the right form in which to regard it. The chief part of the paper is concerned with developing the results given in ‘Nature’; owing to other work I have not carried the matter much farther yet. The main new points are general formulæ for the intensities of spectral lines, and for the magnetic moment, and the form the theory must take for several electrons—in which my first suggestion was wrong, and which Pauli has developed from his point of view. In a future paper I hope to discuss the motion of a free electron in a magnetic field, together with other problems. Since writing the account of the theory in ‘Nature’ I have had the immense benefit of a visit to Prof. Bohr’s Institute in Copenhagen, and have thus enjoyed the advantage of discussing the subject with him, Dr. Klein and the other members in detail. I may take the opportunity here to express my thanks to them for their interest in the matter and for many helpful criticisms.

Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character•Sep 1, 1927•66 citations

State measurement in quantum mechanics

Gennaro Auletta, Mauro Fortunato, Giorgio Parisi A

In classical mechanics, as we know, all observables commute with each other and therefore belong to the same “commuting set.” This means that – in principle – we can measure all observables simultaneously. Then, the state manifests itself as a collection of properties (of values of observables) (see Sec. 1.1), and as such it is observable. On the other hand, quantum-mechanical observables may not commute (see Subsec. 2.1.5). As a consequence, the state is not just a collection of observable values (see also Sec. 2.3) so that we may ask ourselves whether it is observable or not, and therefore raise the following question: What is the nature of the wave function? Is it simply a mathematical tool, i.e. does it only represent the sum of all that we can know about a system? Or does it have an ontological status? Since the early days of quantum mechanics, this question has been very popular. As a first attempt, de Broglie tried to interpret the wave function as describing, in classical terms, a wave field that envelopes a classical particle (see also Subsec. 16.3.2). This theory should predict the existence of empty waves, but several experiments have shown negative results (see also the end of Sec. 9.6). More recently, many physicists have tried to propose some methods in order to measure the wave function. Here we shortly report on some of these proposals and discuss to what extent the quantum state can be measured.

Cambridge University Press eBooks•Apr 16, 2009•0 citations

The fundamental idea of wave mechanics

Erwin Schrödinger

Resonance•Feb 1, 1999•24 citations

Everett’s pure wave mechanics and the notion of worlds

Jeffrey Alan Barrett

Everett ( 1957a , b , 1973 ) relative-state formulation of quantum mechanics has often been taken to involve a metaphysical commitment to the existence of many splitting worlds each containing physical copies of observers and the objects they observe. While there was earlier talk of splitting worlds in connection with Everett, this is largely due to DeWitt’s (Phys Today 23:30–35, 1970 ) popular presentation of the theory. While the thought of splitting worlds or parallel universes has captured the popular imagination, Everett himself favored the language of elements, branches, or relative states in describing his theory. The result is that there is no mention of splitting worlds or parallel universes in any of Everett’s published work. Everett, however, did write of splitting observers and was willing to adopt the language of many worlds in conversation with people who were themselves using such language. While there is evidence that Everett was not entirely comfortable with talk of many worlds, it does not seem to have mattered much to him what language one used to describe pure wave mechanics. This was in part a result of Everett’s empirical understanding of the cognitive status of his theory.

European Journal for Philosophy of Science•Mar 22, 2011•65 citations

The Elements of Wave Mechanics1

L. M. Milne-Thomson

Nature•Jun 1, 1928•4 citations
Abstract In an article in ‘Nature’ last February I put forward a suggestion, of necessity in so concise a form as to be not very easily intelligible, that when the magnetic properties of the atom are regarded from the point of view of the wave mechanics, they suggest that the electron is to be taken as a wave of two components, like light, not of one like sound. The theory and its mathematical development were only outlined in ‘Nature,’ and the object of the present work is to give them in fuller detail. Recently Pauli has published a paper on the same subject, and arrived at the same mathematical results, but owing to the fact that he is more disposed to regard the wave theory as a mathematical convenience and less as a physical reality, he stops short of the point which was the guiding principle to me, and refuses to interpret the two functions that we both obtain as formed from a vector. I shall therefore here develop somewhat fully the arguments and analogies which seem to me to show that the vector is the right form in which to regard it. The chief part of the paper is concerned with developing the results given in ‘Nature’; owing to other work I have not carried the matter much farther yet. The main new points are general formulæ for the intensities of spectral lines, and for the magnetic moment, and the form the theory must take for several electrons—in which my first suggestion was wrong, and which Pauli has developed from his point of view. In a future paper I hope to discuss the motion of a free electron in a magnetic field, together with other problems. Since writing the account of the theory in ‘Nature’ I have had the immense benefit of a visit to Prof. Bohr’s Institute in Copenhagen, and have thus enjoyed the advantage of discussing the subject with him, Dr. Klein and the other members in detail. I may take the opportunity here to express my thanks to them for their interest in the matter and for many helpful criticisms.
In classical mechanics, as we know, all observables commute with each other and therefore belong to the same “commuting set.” This means that – in principle – we can measure all observables simultaneously. Then, the state manifests itself as a collection of properties (of values of observables) (see Sec. 1.1), and as such it is observable. On the other hand, quantum-mechanical observables may not commute (see Subsec. 2.1.5). As a consequence, the state is not just a collection of observable values (see also Sec. 2.3) so that we may ask ourselves whether it is observable or not, and therefore raise the following question: What is the nature of the wave function? Is it simply a mathematical tool, i.e. does it only represent the sum of all that we can know about a system? Or does it have an ontological status? Since the early days of quantum mechanics, this question has been very popular. As a first attempt, de Broglie tried to interpret the wave function as describing, in classical terms, a wave field that envelopes a classical particle (see also Subsec. 16.3.2). This theory should predict the existence of empty waves, but several experiments have shown negative results (see also the end of Sec. 9.6). More recently, many physicists have tried to propose some methods in order to measure the wave function. Here we shortly report on some of these proposals and discuss to what extent the quantum state can be measured.
Everett ( 1957a , b , 1973 ) relative-state formulation of quantum mechanics has often been taken to involve a metaphysical commitment to the existence of many splitting worlds each containing physical copies of observers and the objects they observe. While there was earlier talk of splitting worlds in connection with Everett, this is largely due to DeWitt’s (Phys Today 23:30–35, 1970 ) popular presentation of the theory. While the thought of splitting worlds or parallel universes has captured the popular imagination, Everett himself favored the language of elements, branches, or relative states in describing his theory. The result is that there is no mention of splitting worlds or parallel universes in any of Everett’s published work. Everett, however, did write of splitting observers and was willing to adopt the language of many worlds in conversation with people who were themselves using such language. While there is evidence that Everett was not entirely comfortable with talk of many worlds, it does not seem to have mattered much to him what language one used to describe pure wave mechanics. This was in part a result of Everett’s empirical understanding of the cognitive status of his theory.