Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Deriving the De Broglie Wavelength

  1. Aug 30, 2010 #1
    E=mc^2 and E=hf. In Special Relativity, how can y=h/p be derived from E=hf?
  2. jcsd
  3. Aug 30, 2010 #2
    E2(p) = m2 c4 + p2 c2 [energy in the reference frame with momentum p]

    E(p)=h/T(p) [T(p) is the time periodicity in the reference frame p ]

    m c2 = E(0) [the mass is the energy in the rest frame p=0]

    m c2 = h/T(0) [T(0) is the time periodicity in the reference frame p=0]

    by putting all things together you find:

    1/T2(p) = 1/T2(0) + c2/y2(p) [from the relativistic dispersion relation]

    where y(p)= h / p [is the induced spatial periodicity in the reference frame with momentum p].

    See http://arxiv.org/abs/0903.3680" [Broken] "Compact time and determinism: foundations"

    Then if you impose the above periodicities as constraints to a string (field in compact space-time, similarly to the harmonic frequency spectrum of a vibrating string with fixed ends) you obtain the following energy quantization

    E2n(p) = n2 E2(p) = n2( M2 c4 + p2 c2)

    which is actually the energy quantization coming from the usual field theory with second quantization, after normal ordering. In arXiv:0903.3680 it is shown that this procedure provides an exact matching with ordinary quantum field theory, including Path integral and the commutation relations.
    Last edited by a moderator: May 4, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook