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I have a rather general question regarding the theory of Quantum Mechanics. To preface this question, consider a violin string. When a violinist exposes the string to a bow, this is exposing the string to a wide range of frequencies. In response to this excitation, the string resonates at rather distinct frequencies. In other words, the energy spectrum of a violin string can be understood as a linear combination of distinct energies(frequencies). Why would it not be possible to develop an accurate atomic physics model based on resonant orbital electronic frequencies including possibly spin-orbit resonances as well?

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Actually, "resonant orbital frequencies" is a central idea in quantum mechanics. Schrödinger's equation is a wave equation. Niels Bohr's original model of the atom involves "resonant" electron orbits that contain an integer number of de Broglie wavelengths. –  Nathan Reed Mar 13 '13 at 2:37
    
Agreed, some of these ideas were central to the original developments in the old quantum theory. I'm just curious why such a drastic departure from these classical notions took place since then. If discretization or quantization can be understood in terms of resonance then why not? If the electron spin can be thought of as a classical magnetic moment then why not? –  JEM Mar 13 '13 at 2:45
    
Because electrons can't (just) be waves, because you can measure their position and localize them, count them, etc. like a discrete particle. The question of how can something behave like a wave at times but behave like a particle at other times is the basic dilemma that forced QM to be developed. –  Nathan Reed Mar 13 '13 at 2:50
    
Have you not heard of the string theory revolution?en.wikipedia.org/wiki/String_theory . Why do you think they are called strings? Because particles are the result of vibrations of the string in ten on eleven dimensions, characterized by their quantum numbers one to one. –  anna v Mar 13 '13 at 5:25

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Why would it not be possible to develop an accurate atomic physics model based on resonant orbital electronic frequencies including possibly spin-orbit resonances as well?

Classical wave equations cannot describe an electron around a hydrogen atom etc because classically the electron in a circular orbit would loose energy by radiation and spiral down into the nucleus. ( see paragraph 20-4 in "classical electricity and magnetism" by Panofski and Philips, radiation from circular orbits)

Any classical solution would have the same fate, whether superpositions or what not. This is the basic reason why quantum mechanical intuition was developed.

After the Bohr model which constrained axiomatically the electrons into orbits the Schrodinger equation merged the concepts of resonance, so evident in the atomic spectra measurements, with the concept of probability distributions: The electrons are in orbitals, not orbits, and the wavefunction of the solution of the quantum mechanical equation gives the probability of finding a particle with (x,y,z,t) or (p_x,p_y,p_z,E). The solution does not describe the coordinate position as a classical wave equation, there is no correspondence.

Nevertheless, the classical string has a comeback into the theory of elementary particles as string theory, with ten or eleven dimensions:

String theory posits that the electrons and quarks within an atom are not 0-dimensional objects, but made up of 1-dimensional strings. These strings can oscillate, giving the observed particles their flavor, charge, mass, and spin.

The standard model of elementary particles is embedded into the string group symmetries structure, where the particles themselves are excitation modes of a string.

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Thank you Anna for the comments. I have one more "classical" resonance issue to pose then a few questions concerning your string theory ideas. Resonance: would it be possible to develop some physical ideas concerning classical resonance and permissible periodic orbits in such a way that the interaction of the atomic system with the "bow" ie. light, has the effect of maintaining the conservation of energy? As far as string theory is concerned, i have been under the impression that the string objects are extremely small. several orders of magnitude smaller than an atomic nucleus. –  JEM Mar 15 '13 at 4:54
    
Are the particles and their properties some sort of emergent phenomena arising from the interaction of many strings?? The dimension requirements (10 or 11) are physically relevant or facilitate computations or something else? –  JEM Mar 15 '13 at 5:01
    
The Bohr atom axiomatically conserved energy to this purpose but it was superseded by the potential well solutions of the Schroedinger equations: en.wikipedia.org/wiki/Bohr_atom . You see "light" is also a quantum mechanical object . Classically it runs away with velocity c, cannot be held. –  anna v Mar 15 '13 at 5:04
    
strings are tiny, of Planck length, order of 10^-36 meters, one dimensional entities moving in ten or eleven dimensions. The extra dimensions are necessary for their group structure which can identify all the quantum numbers of the standard model particles, one to one, with excitations of the string. Stable particles are on stable excitations. en.wikipedia.org/wiki/String_theory –  anna v Mar 15 '13 at 5:10
    
Very nice. Looks like string theory is promising. Wondering if ideas from complex systems or nonlinear dynamics could help the elementary particles and their properties "emerge" without the extra dimensions. Thank you very much. I have some catching up to do in the string theory world. –  JEM Mar 15 '13 at 5:48

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