The Zeeman Effect and Stark Effect of Hydrogen in Wave Mechanics; The Force Equation and the Virial Theorem in Wave Mechanics

1928 ◽  
Vol 31 (4) ◽  
pp. 533-538 ◽  
Author(s):  
Arthur Edward Ruark
Keyword(s):  
Virial Theorem ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Wave Mechanics ◽  
Force Equation

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 Patterns and paschen-back analogue in the stark-effect for neon

1929 ◽  
Vol 123 (791) ◽  
pp. 80-103 ◽  
Keyword(s):  
Quantum Number ◽  
Stark Effect ◽  
Selection Rule ◽  
Theoretical Calculations ◽  
Zeeman Effect ◽  
Final States ◽  
Outer Electron ◽  
Initial State ◽  
Final State ◽  
Left Handed

While the Stark-effect has not been studied so extensively as the Zeeman-effect, either in the experiments or in their interpretations, many of the more prominent features have been observed and have received adequate explanation on the quantum theory. Among these may be mentioned the patterns characteristic of the different series in the singlet system of parhelium. The variety of observed patterns in the Stark-effect, as contrasted with the normal Zeeman-effect found for all series of this system, arises from a differential action of the external electric field on the initial and final states, and a breaking down of the usual selection rule for the azimuthal quantum number. Some simplification is brought about, however, by the fact that only the absolute value of the quantum number m has any meaning in the interpretation of these photographs, since the action of the field is the same for right or left-handed motion of the outer electron in its orbit. This results in asymmetrical patterns for all the lines. The number of components observed in the patterns of individual lines of parhelium is in accord with the theoretical view that the vector j (here equal to l ) is resolved along the direction of the applied field to give the integral m values ranging from - j to + j , and that the usual selection rule holds for m . The displacements and intensities are in excellent agreement with the theoretical calculations based on the perturbation theory of quantum mechanics. The spacing of the sub-levels identified by ± m in the initial state is decidedly irregular in the Stark-effect as compared with the normal Zeeman-effect, where the displacements are proportional to m . The Zeeman order of the levels is usually reversed, in fact, and the spacing is uneven. Displacements in the final state are theoretically very small, and have not been observed with certainty. In the Stark-effect for orthohelium (triplet system) the same group of patterns was observed. An explanation of these observations, which is slightly less satisfactory than that obtained with parhelium, has been made by similar methods, neglecting the electron spin. Thus the m values were again given ranges determined in each case by the l of the outer electron, and not by the j for the whole atom. Most of the plates failed to reveal any of the fine structure of the normal orthohelium spectrum.

scholarly journals The Zeeman effect and spherical harmonics

1927 ◽  
Vol 115 (770) ◽  
pp. 1-19 ◽  
Keyword(s):  
Recent Work ◽  
Spherical Harmonics ◽  
Strong Field ◽  
Zeeman Effect ◽  
Simple System ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Wave Mechanics ◽  
Matrix Methods ◽  
The Matrix

1. The chief object of the present paper is to present a simple system of equations which are competent to determine the frequencies and intensities of the lines in the standard Zeeman effect. By the standard Zeeman effect is meant the type where the terms are given by Landé’s " g "and “γ” formulæ, and where the multiplicity of the two sets of terms is the same. It will probably be held that the theory of such multiplets has been fairly completely understood for the last two years owing to the works of Sommerfeld, Heisenberg, Landé and Pauli, and the main new contribution of the present work is that, whereas these writers gave formulæ valid only either in weak or strong field (except for doublets, where Heisenberg and Jordan give the value for any strength), here we have complete formulæ from which the intensity of any component in any strength of field can be obtained merely from the solution of rather simple algebraic equations. The proper attack on this problem would undoubtedly be by way of the recent work of Heisenberg on the helium spectrum, and his still more recent work on complex spectra; but this theory is still in the making, so that it has not been practicable to apply it here, and to this extent our results are unverified. Their validity rests firstly on a complete verification of all known facts connected with both weak and strong fields (and intermediate fields for doublets), and also on a conformity with the general features of wave mechanics. The work of Heisenberg and Jordan could readily have been adapted to give all the results of the present paper; but it would have been harder to follow because the matrix methods are not so easy for most readers as are spherical harmonics.

Comment on the Analysis of Microwave Rotational Zeeman Effect Spectra of Symmetric Top Molecules

1975 ◽  
Vol 30 (10) ◽  
pp. 1265-1270 ◽  
Author(s):  
L. Engelbrecht ◽  
D.H. Sutter
Keyword(s):  
Stark Effect ◽  
Previous Analysis ◽  
Zeeman Effect ◽  
Numerical Results ◽  
First Order ◽  
Internal Rotations ◽  
Rotational Transitions ◽  
Symmetric Top Molecules

Abstract It is pointed out that the translational Lorentz effect which has been neglected in all previous analysis of rotational Zeeman spectra has considerable effects on the overall appearance of the Zeeman multiplets if the rotational transitions show first order Stark effect. This situation occurs for symmetric tops and for E-species transitions of molecules with low barrier internal rotations. Inclusion of the translational Lorentz effect leads to corrections to the published g‖-values of symmetric tops which are far outside the quoted experimental uncertainties. As an example numerical results are given for CH3F and CH3CCH.

scholarly journals Half-integral quantum numbers in the theory of the stark effect and a general hypothesis of fractional quantum numbers

1924 ◽  
Vol 105 (734) ◽  
pp. 641-650 ◽  
Keyword(s):  
Stark Effect ◽  
Zeeman Effect ◽  
Fractional Quantum ◽  
General Hypothesis ◽  
Quantum Numbers ◽  
Considerable Success ◽  
Anomalous Zeeman Effect ◽  
Band Spectra ◽  
Fractional Quantum Numbers ◽  
Integral Quantum

1. Indications of the occurrence of fractional quantum numbers have already been found by Kratzer from a study of certain band spectra, and by Curtis in his experimental investigation of helium bands. Heisenberg has also employed half-integral numbers in a quantum theory of the anomalous Zeeman effect with considerable success. The fourth of the slightly extended quantum conditions recently suggested by W. Wilson and applied by the present writer to the Zeeman effect involves a fractional quantum number, as O. W. Richardson has pointed out. K. F. Niessen, in his work on the positively ionised hydrogen molecule, observes certain discontinuities in the energy graphs between symmetrical and asymmetrical models which strongly the occurrence of half-integral quantum orbits for the latter. He refrains, however, from making this assumption, on the ground that it would necessitate the adoption of half numbers in the somewhat allied case of the Stark effect.

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