The Quantum Oscillatory Modulated Potential Ⅰ- The Hydrogen Atom


In this work we are presenting a modified Coulomb potential function to describe the interaction between two micro-scopic electric charges. In particular, concerning the interaction between the proton and the electron in the hydrogen atom. The modified potential function is the product of the classical Coulomb potential and an oscillatory function dependent on a quantized phase factor. The oscillatory function picks up only selected points along the Coulomb potential, creating potential wells and barriers around the nucleus of the atom. The new potential reveals us new features of the hydrogen atom. Searching for a manner to determine the phase factor, we are using the concept of the de Broglie particle wavelike behavior and the quantum analogue of the virial theorem for describing the bound motion of a particle in a central force field. This procedure is a kind of feedback action, where we are making use of well established concepts of the quantum mechanics aiming to determine the phase factor of the new interaction potential.

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W. Filho, "The Quantum Oscillatory Modulated Potential Ⅰ- The Hydrogen Atom," Journal of Modern Physics, Vol. 3 No. 7, 2012, pp. 597-603. doi: 10.4236/jmp.2012.37081.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] R. P. Feymann, R. B. Leighton and M. Sands, “Lectures on Physics,” Addison Wesley, Reading, 1966.
[2] C. Cohen-Tannoudji, B. Diu and F. Lalo?, “Quantum Mechan-ics,” John Wiley & Sons, New York, 1997.
[3] L. Gilder, “The Age of Entanglemen,” Alfred A. Knopf, New York, 2008.
[4] W. W. Filho, “Mecanica Quantica,” Editora da UFG, Goiania, 2002.
[5] R. M. Eisberg, “Fundamentals of Modern Physics,” John Wiley & Sons Inc., New York, 1961.
[6] P. A. Tipler, “Modern Physics,” Worth Publishers, Inc. Irving, 1986.
[7] L. Pauling and E. B. Wilson, “Introduction to Quantum Me-chanics,” McGraw Hill, New York, 1935.
[8] W. Hauser, “Introduction to the Principles of Electromagnetism,” Addison Wesley Publishing Company Inc., Boston, 1970.
[9] E. Merzbacher, “Quantum Mechanics,” John Wiley & Sons Inc., New York, 1976.
[10] V. A. Fock, “Fundamentals of Quantum Mechanics,” Mir Pub-lishers, Moscow, 1982.

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