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Derivation of De Broglie wavelength

by PhiJ
Tags: broglie, derivation, wavelength
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PhiJ
#1
Oct26-05, 09:46 AM
P: 41
The De Broglie wavelength was derived like this by our physics teacher.
E=hf v=fλ E=mc^2
so
hf=mc^2
hv=λmc^2
Then the WRONG BIT
h=λmv
h=λρ
λ=h/ρ

But that only works for light (when c=v). There must be a correct way of deriving it for electrons etc. We are expected to use this for electrons.
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Hans de Vries
#2
Oct26-05, 05:07 PM
Sci Advisor
P: 1,135
Quote Quote by PhiJ
The De Broglie wavelength was derived like this by our physics teacher.
E=hf v=fλ E=mc^2
so
hf=mc^2
hv=λmc^2
Then the WRONG BIT
h=λmv
h=λρ
λ=h/ρ
But that only works for light (when c=v). There must be a correct way of deriving it for electrons etc. We are expected to use this for electrons.
It only works if you take: wave-speed = [itex]\frac{c^2}{v}[/tex] where v is the physical
speed of the electron, this is however an ad-hoc assumption here. It's not
that hard to derive λ=h/ρ directly from E=hf but it takes Special Relativity:

http://www.chip-architect.com/physics/deBroglie.pdf


Regards, Hans


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