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Particle in a Box Question .

  1. Sep 30, 2014 #1
    I've been wondering, if an electron in a box (of length L) is NOT a wave, what is the probability density in this non-quantum mechanical case?
     
  2. jcsd
  3. Sep 30, 2014 #2

    bhobba

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    Non Quantum Mechanical case - don't get it.

    But its not a wave in any usual physical sense. To see it the wave propagates in an abstract infinite dimensional Hilbert space.

    The wave particle duality is a crock of the proverbial that was outdated when Dirac came up with his transformation theory in about 1927.

    It persists today purely because of the semi-historical approach most textbooks take.

    To see the real basis of QM check out:
    http://www.scottaaronson.com/democritus/lec9.html

    For a correct treatment of QM have a look at the first 3 chapters of Ballentine - it may be a revelation - it was for me:
    https://www.amazon.com/Quantum-Mechanics-A-Modern-Development/dp/9810241054

    Thanks
    Bill
     
    Last edited by a moderator: May 7, 2017
  4. Sep 30, 2014 #3

    Nugatory

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    The electron is never a wave, no more so in quantum mechanics than in classical mechanics. Bhobba's observation about a "crock of the proverbial..." is indelicate but accurate.

    But you're asking about the probability density for the position of the electron when quantum effects are insignificant. That will be ## \rho(x)=\delta(x-X)## where ##X## is the classical position and ##\delta## is the Dirac delta function. This solution is not physically realizable, although it is easy to construct situations (for example, all of classical mechanics) where it's a useful idealization.
     
    Last edited: Sep 30, 2014
  5. Sep 30, 2014 #4
    Thank you!!!!!!! I think I get it.
     
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