De Broglie Wavelength Derivation

  • Thread starter Goalie33
  • Start date
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.
 

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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