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Add another anchor to the anchored string.

  1. May 3, 2009 #1
    Add another "anchor" to the anchored string.

    Consider a vibrating string that has an additional sideways restoring force per unit length, the magnitude of the force is proportional to the sideways displacement. This string will have the same dispersion curve of a massive quantum. See:

    Iain G. Main, Vibrations and Waves in Physics, 3rd ed., Cambridge University Press, 1993, pages 224-229.

    Let us add an additional sideways force per length perpendicular to the first. Let the string move in two dimensions now. Let the displacement of the string in these two dimensions be given by a complex number. The motion of the string is given by a function of time and position along the string. I guessing:


    This string will have 2 "orthogonal" sets of solutions which together can be used to come up with a general solution of this system. All solutions to the wave equation of this string, taken as a whole, can be rotated about the length of the string by some angle and this new set can be mapped one to one with the old set, rotating the set of solutions produces the same set of solutions. Any solution to the wave equation of this string can be rotated about the length of the string and we still have the "same" physics. We can have "linearly polarized" waves and "circularly polarized" waves and all polarizations in between.

    Now do this again for the three dimensional analog, the 3D bi-anchored string.

    Do we get any interesting physics for the 3D case?

    Thanks for your thoughts or corrections.

    From:

    http://en.wikipedia.org/wiki/Quantum...al_formulation [Broken]

    ...
    In the mathematically rigorous formulation of quantum mechanics, developed by Paul Dirac[7] and John von Neumann[8], the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors") residing in a complex separable Hilbert space (variously called the "state space" or the "associated Hilbert space" of the system) well defined up to a complex number of norm 1 (the phase factor).
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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