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

Proceedings of the Royal Society of Edinburgh

XIV.—Note on Professor Whittaker's Quantum Mechanism in the Atom

R. A. Houstoun

Published Jan 1, 1923• 0 citations
Publisher

Abstract

It seems desirable to check Professor Whittaker's model numerically; algebraical expressions when evaluated sometimes have the wrong order of magnitude. Let us suppose that initially the magnet system is at rest, and that the electron starts from the origin with velocity u.
DOI
10.1017/s0370164600023920

Related papers

XI.—Note on Professor Whittaker's Paper “On the Quantum Mechanism in the Atom”

John Ewing

In Professor Whittaker's highly interesting and suggestive application of my model the postulated structure is a system of magnets rigidly connected like the spokes of a wheel, having poles of the same name at the circumference, the corresponding poles of contrary name being all at the centre. He shows that when a bombarding electron, moving in the direction of the axis, approaches such a wheel it sets the wheel turning, the rotation of the poles constituting what he calls a “magnetic current.” If the initial velocity of the bombarding electron falls short of a certain limiting value, the encounter is perfectly elastic, and the electron is reflected back without loss of energy; the point at which its direction of motion becomes reversed may be on either side of the plane of the wheel, depending on the electron's initial velocity of approach. If the initial velocity exceeds the stated limit, the electron passes clear through the system and escapes, but with a definite reduction of velocity, corresponding to a quantum of energy which it has given up to the wheel. When the encounter is elastic, the angular velocity which the wheel acquires during the approach of the electron is lost during the return of the electron. When the encounter is not elastic, and the electron has passed clear through, the wheel is left with an angular velocity ω; and the energy which that represents is the source of the consequent radiation.

Proceedings of the Royal Society of Edinburgh•Jan 1, 1923•1 citation

The Whittaker Quantum Mechanism

F. E. Kester

peated periodic process, I was led to a discussion of the latter integral for the special case of an isolated magnet pole, the Dirac1 quantum m, carried in a closed linking with a closed of an elementary charge of electricity e. The analogy is the more interesting in that the two functions here involved are useful in expressing, by minimum values of each, the conditions for of mechanical systems in conservative fields of force-the potential energy function at minimum value for static equilibrium, the Maupertuis function, evaluated for the natural path of a system between any two configurations, at minimum value for kinetic equilibrium with the field for this path. Whittaker2 discussed the interchanges of energy occurring in the special case of an electron flying along the axis of a magnetic wheel the spokes of which are magnets with their south poles (say) at the center, the north poles at the rim. The expedient of placing one set of poles at the axis to avoid the magnetic action of the flying electron upon them is, of course, not feasible. Lorentz3 corrected this feature of the Whittaker mechanism by assuming an isolated pole, giving it the form of a plane circular filament, closed on itself and free to move only in rotation about its own axis, and he generalized the problem to cover any form of the electron's which may link with the filament.

Transactions of the Kansas Academy of Science•Mar 28, 1935•0 citations

XV.—The Importance of Professor Whittaker's Atomic Model and of other Atomic Models

William Peddie

The atom, even in its simplest form, must possess a most complicated structure. The aim of physical science is to find a hypothetical structure, and mode of its functioning, which will give a good account of atomic phenomena. When the phenomena are complicated, and only very partially known, hypothetical investigations are most uncertain and provisional, and make little attempt to work otherwise than by analogy or illustration. In such cases help is often obtained through the discovery of a general law which unifies a wide range of phenomena, and which may be followed by many diverse structures in their activities. Well-known examples are found in the law of conservation of energy, the law of least action, and, recently, the law of quantum action.

Proceedings of the Royal Society of Edinburgh•Jan 1, 1923•0 citations

Some remarks on the quantum mechanics of the electron

Gottfried Möllenstedt

Physica B+C•Jul 1, 1988•4 citations

Origin of the spin-orbit interaction (Presentation Recording)

Gianfranco Spavieri, Masud Mansuripur

We consider a semi-classical model to describe the origin of the spin-orbit interaction in a simple system such as the hydrogen atom. The interaction energy U is calculated in the rest-frame of the nucleus, around which an electron, having linear velocity v and magnetic dipole-moment μ, travels in a circular orbit. The interaction energy U is due to the coupling of the induced electric dipole p=(v/c)×μ with the electric field En of the nucleus. According to quantum mechanics, the radius of the electron’s orbit remains constant during a spin-flip transition. Under such circumstances, our model predicts that the energy of the system changes by ΔE=1/2U, the factor 1/2 emerging naturally as a consequence of equilibrium and the change of the kinetic energy of the electron. The correct 1/2 factor for the spin-orbit coupling energy is thus derived without the need to introduce the well-known Thomas precession in the rest-frame of the electron.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 11, 2015•0 citations

ON THE QUESTION OF INTERPRETATION OF THE DIRAC EQUATION FOR THE ELECTRON

Г. А. Зайцев

Zhur. Eksptl'. i Teoret. Fiz.•Aug 1, 1955•0 citations
In Professor Whittaker's highly interesting and suggestive application of my model the postulated structure is a system of magnets rigidly connected like the spokes of a wheel, having poles of the same name at the circumference, the corresponding poles of contrary name being all at the centre. He shows that when a bombarding electron, moving in the direction of the axis, approaches such a wheel it sets the wheel turning, the rotation of the poles constituting what he calls a “magnetic current.” If the initial velocity of the bombarding electron falls short of a certain limiting value, the encounter is perfectly elastic, and the electron is reflected back without loss of energy; the point at which its direction of motion becomes reversed may be on either side of the plane of the wheel, depending on the electron's initial velocity of approach. If the initial velocity exceeds the stated limit, the electron passes clear through the system and escapes, but with a definite reduction of velocity, corresponding to a quantum of energy which it has given up to the wheel. When the encounter is elastic, the angular velocity which the wheel acquires during the approach of the electron is lost during the return of the electron. When the encounter is not elastic, and the electron has passed clear through, the wheel is left with an angular velocity ω; and the energy which that represents is the source of the consequent radiation.
peated periodic process, I was led to a discussion of the latter integral for the special case of an isolated magnet pole, the Dirac1 quantum m, carried in a closed linking with a closed of an elementary charge of electricity e. The analogy is the more interesting in that the two functions here involved are useful in expressing, by minimum values of each, the conditions for of mechanical systems in conservative fields of force-the potential energy function at minimum value for static equilibrium, the Maupertuis function, evaluated for the natural path of a system between any two configurations, at minimum value for kinetic equilibrium with the field for this path. Whittaker2 discussed the interchanges of energy occurring in the special case of an electron flying along the axis of a magnetic wheel the spokes of which are magnets with their south poles (say) at the center, the north poles at the rim. The expedient of placing one set of poles at the axis to avoid the magnetic action of the flying electron upon them is, of course, not feasible. Lorentz3 corrected this feature of the Whittaker mechanism by assuming an isolated pole, giving it the form of a plane circular filament, closed on itself and free to move only in rotation about its own axis, and he generalized the problem to cover any form of the electron's which may link with the filament.
The atom, even in its simplest form, must possess a most complicated structure. The aim of physical science is to find a hypothetical structure, and mode of its functioning, which will give a good account of atomic phenomena. When the phenomena are complicated, and only very partially known, hypothetical investigations are most uncertain and provisional, and make little attempt to work otherwise than by analogy or illustration. In such cases help is often obtained through the discovery of a general law which unifies a wide range of phenomena, and which may be followed by many diverse structures in their activities. Well-known examples are found in the law of conservation of energy, the law of least action, and, recently, the law of quantum action.
We consider a semi-classical model to describe the origin of the spin-orbit interaction in a simple system such as the hydrogen atom. The interaction energy U is calculated in the rest-frame of the nucleus, around which an electron, having linear velocity v and magnetic dipole-moment μ, travels in a circular orbit. The interaction energy U is due to the coupling of the induced electric dipole p=(v/c)×μ with the electric field En of the nucleus. According to quantum mechanics, the radius of the electron’s orbit remains constant during a spin-flip transition. Under such circumstances, our model predicts that the energy of the system changes by ΔE=1/2U, the factor 1/2 emerging naturally as a consequence of equilibrium and the change of the kinetic energy of the electron. The correct 1/2 factor for the spin-orbit coupling energy is thus derived without the need to introduce the well-known Thomas precession in the rest-frame of the electron.