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Quantum Spherical Harmonics

  1. Aug 1, 2014 #1

    As a science writer, I've tasked myself with acquiring a thorough theoretical and historical understanding
    of Quantum Mechanics.

    It would be interesting to know if there has ever been any experimental verification of Laplace's
    spherical harmonics, relating to the quantum mechanical model of the atom; Or if spherical harmonics
    are purely a theoretical mathematical solution to 3 dimensional cartesian electron orbital locations
    at the various quantum energy levels.

    It would also be interesting to know which experimental discovery lead to the abandonment of Bohr's planetary model
    of the atom, in old quantum mechanics, the scientists who performed the experiment, as well as the date and location
    the experiment occured, and the process through which this discovery lead to the current quantum model.

    Kind regards,

    A. Holtz

  2. jcsd
  3. Aug 1, 2014 #2


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    "On 16 November, in another letter, Schrödinger wrote:-

    I have been intensely concerned these days with Louis de Broglie's ingenious theory. It is extraordinarily exciting, but still has some very grave difficulties.

    One week later Schrödinger gave a seminar on de Broglie's work and a member of the audience, a student of Sommerfeld's, suggested that there should be a wave equation. Within a few weeks Schrödinger had found his wave equation. "
  4. Aug 1, 2014 #3


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    One problem with old quantum theory and the Bohr-Sommerfeld quantization is that it could only quantize 'integrable' systems, which are systems in which all motions are periodic. I don't know if that was part of Schrodinger's motivation in searching for his equation. Einstein did know of this limitation of the Bohr-Sommerfeld quantization. http://homepages.ulb.ac.be/~gaspard/G.quantum.Encycl.05.pdf
  5. Aug 2, 2014 #4

    Thank you for the Quantum Theory PDF link atyy, this is quite interesting.

    The only missing information is the experimental basis for Einstein's conclusion
    that the Helium atom is a classically non-integrable system.

    "In 1917, Albert Einstein pointed out that the Bohr–Sommerfeld quantization rule cannot be applied to classically non-integrable systems (such as helium atom), and it slowly became apparent that radically new ideas were required."

    Thus far, I've been unable to find any scientific publications confirming the spherical harmonic fields
    predicted by Schrödinger wave functions. Perhaps not surprising given the technical challenges.

    Last edited: Aug 2, 2014
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