THE THEORY OF THE ANOMALOUS ZEEMAN EFFECT ON THE NEW MECHANICS

2011 ◽  
pp. 194-202
Author(s):  
George Birtwistle
Keyword(s):  
Zeeman Effect ◽  
Anomalous Zeeman Effect

Phenomenology of noncommutative phase space via the anomalous Zeeman effect in hydrogen atom

2014 ◽  
Vol 29 (31) ◽  
pp. 1450177 ◽  
Author(s):  
Willien O. Santos ◽  
Andre M. C. Souza
Keyword(s):  
Phase Space ◽  
Hydrogen Atom ◽  
Zeeman Effect ◽  
Nonrelativistic Limit ◽  
Noncommutative Phase Space ◽  
G Factor ◽  
First Order ◽  
Anomalous Zeeman Effect ◽  
Space Noncommutativity ◽  
First Order Perturbation

The Hamiltonian describing the anomalous Zeeman effect for the hydrogen atom on noncommutative (NC) phase space is studied using the nonrelativistic limit of the Dirac equation. To preserve gauge invariance, space noncommutativity must be dropped. By using first-order perturbation theory, the correction to the energy is calculated for the case of a weak external magnetic field. We also obtained the orbital and spin g-factors on the NC phase space. We show that the experimental value for the spin g-factor puts an upper bound on the magnitude of the momentum NC parameter of the order of [Formula: see text], 34 μ eV /c. On the other hand, the experimental value for the spin g-factor was used to establish a correction introduced by NC phase space to the presently accepted value of Planck's constant with an uncertainty of 2 part in 1035.

Failures

2019 ◽  
pp. 300-382
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Ground State Energy ◽  
Ground State ◽  
Equations Of Motion ◽  
Zeeman Effect ◽  
Stationary States ◽  
Old Quantum Theory ◽  
History Of ◽  
Anomalous Zeeman Effect

We consider three topics which proved frustratingly resistant to the methods of the old quantum theory up to the point of emergence of the quantum mechanics of Heisenberg and collaborators in late 1925. First, the old theory could not account convincingly for the superfluity of stationary states implied by the existence of the complex multiplets seen in most atomic spectra. Second, the progressively more complicated theories proposed for explaining the splittings of lines in the anomalous Zeeman effect were found to lead inevitably to glaring inconsistencies with the assumed mechanical equations of motion. Finally, there was the problem of the dual spectrum of helium, and even more basically, of the ground state energy of helium, all calculations of which in terms of specified electron orbits gave incorrect results. We relate the tangled history of the efforts to provide a theoretical resolution of these problems within the old quantum theory.

The Heisenberg Theory of the Anomalous Zeeman Effect

Nature ◽  
1923 ◽  
Vol 112 (2811) ◽  
pp. 396-396 ◽  
Author(s):  
G. BREIT
Keyword(s):  
Zeeman Effect ◽  
Anomalous Zeeman Effect

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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