• Corpus ID: 15422334

Rise and fall of the old quantum theory

@article{Bucher2008RiseAF,
  title={Rise and fall of the old quantum theory},
  author={Manfred Bucher},
  journal={arXiv: History and Philosophy of Physics},
  year={2008}
}
  • M. Bucher
  • Published 11 February 2008
  • Physics
  • arXiv: History and Philosophy of Physics
The old quantum theory of Bohr and Sommerfeld was abandonned for the wrong reason. Its contradictions were caused not by the orbit concept but by a mental barrier--the inconceivability that an electron might collide with the atomic nucleus. Removing that barrier resolves the theory's main failures--incorrect orbital momenta, He atom, H2+ molecule ion. The inclusion of electron oscillations through the nucleus--a concept called "Coulomb oscillator"--renders the old quantum theory consistent with… 

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References

SHOWING 1-10 OF 67 REFERENCES

Coulomb oscillations as a remedy for the helium atom

The largest failure of the old, Bohr-Sommerfeld quantum theory was with the helium atom. It brought about the theory's demise. I show that this failure does not originate, as commonly believed, with

The quantum theory of the electron

The new quantum mechanics, when applied to the problem of the structure of the atom with point-charge electrons, does not give results in agreement with experiment. The discrepancies consist of

Semiclassical quantization of the low lying electronic states of H2

The classical dynamics of an electron moving in the presence of two equally charged, fixed nuclei is presented. The manner in which the values of the three constants of the motion determine the

Chaos in classical and quantum mechanics

Contents: Introduction.- The Mechanics of Lagrange.- The Mechanics of Hamilton and Jacobi.- Integrable Systems.- The Three-Body Problem: Moon-Earth-Sun.- Three Methods of Section.- Periodic Orbits.-

Coulomb oscillation in the hydrogen atom and molecule ion

Semiclassical oscillation of the electron through the nucleus of the H atom yields both the exact energy and the correct orbital angular momentum for l=0 quantum states. Similarly, electron

Introduction to Quantum Mechanics

I. THEORY. 1. The Wave Function. 2. The Time-Independent Schrodinger Equation. 3. Formalism. 4. Quantum Mechanics in Three Dimensions. 5. Identical Particles. II. APPLICATIONS. 6. Time-Independent

The electron inside the nucleus: an almost classical derivation of the isotropic hyperfine interaction

The Fermi contact term of the hyperfine interaction is derived with a minimum of quantum mechanical assumptions and the use of two different length scales. The latter approach clarifies the

The Physical Nature of the Chemical Bond

The quantum mechanical wave functions of molecules are discussed. An attempt is made to effect a simultaneous regional and physical partitioning of the molecular density, the molecular pair density,

Interaction potentials for AgCl and AgBr

We present interaction potentials for AgCl and AgBr derived from quantum-mechanical approximations and fitted to the experimental lattice constant and energy, elastic and dielectric constants, and

Die Mechanik des Himmels

THE number of text-books on the subject of celestial mechanics is by no means so large but that an addition ought to be warmly welcomed. More especially is this the case when the author is one who
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