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De Broglie Wavelength Derivation

  1. Mar 20, 2009 #1
    In Classical Mechanics the derivative of Kinetic energy with respect to velocity is momentum, so I was wondering if this is valid:

    In this L is lambda or wavelength and h is Planck's Constant.

    E=hf, therefore E=h(v/L)
    This means that dE/dv=h/L.(h and L are constants and the derivative of v would be 1.)
    Rearranging this we get:
    L=h/p.

    I just wanted to know if this is considered valid.
     
  2. jcsd
  3. Mar 21, 2009 #2

    malawi_glenn

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    in E=hf, 'v' is equal to c, which is a constant!

    One does not 'derive' de Broglie Wavelength, one postulates it.

    E = hc/L, E/c = h/L

    But E/c is the momentum of a massless particle, e.g. the photon. Hence, we postulate that this result can be more general to be valid for massive particles with momentum p.

    p = h/L

    So it is not a rigour derivation, but a bold postulate, which turned out to work fine :-)
     
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