Re: de broglie wave velocity
- From: srp@xxxxxxxxxxxx
- Date: 17 Nov 2006 09:30:33 -0800
Edward Green a écrit :
srp@xxxxxxxxxxxx wrote:
richardskaa@xxxxxxxxxxxxx a écrit :
<...>
So wave velocity = mc2/h. h/mv
= mc2/ mv
= c2/v
Well, if you consistantly substitute with relativistic p,
this is not what you get.
It seems to me I got this result by a different route in the past. I
think I started with one of the relativistic wave equations, and simply
directly evaluated the phase and group velocities (I claim at the time
I hadn't seent the relativistic wave equations, but simply tried
generalizing the Schrodinger equation, but that's another story).
Regardless, I think v_p v_g = c^2 for de Broglie waves is accepted,
and appears in his original thesis.
Yes. I admit I always was intrigued by this.
To be more precise about my reservation with Richards...
sequence, that appears fine at first reading is this.
p (momentum) of the particle specifically relates to
the carrying energy of the moving particle plus the energy
accounting for the relativistic mass increase of the particle.
Easily verified by using real figures and calculating E=pv
When the OP equates mc^2=hf, the frequency obtained (f) is that
of the energy accounting for the total relativistic mass of the
moving particle, excluding the carrying energy.
When later, he calculate L from h/mv, he obtains a debroglie
wavelength related to the carrying energy plus the energy
accounting for the relativistic "mass increase" of the particle.
ref E=pv
When he then equates wave velocity with fL
he is associating the frequency of the energy accounting for the
total relativistic mass of the moving particle (excluding the
carrying energy) to the debroglie L of the carrying energy
plus the energy accounting for the relativistic "mass increase"
of the particle.
My reservation is that it seems to me that both f and L
should be those of the same "quantity of energy" to be
meaningful.
Unless I am missing something here, it seems to me that
f and L pertaining to two different "quantities of energy" cast
doubts as to the validity of the final "wave velocity = c^2/v
Since relativistic velocities and mass increase can be
calculated only from a particular exponential ratio of carrying
energy over carried energy, it seems to me embedding
exponentials into apparently non exponential terms is
quite risky.
André Michaud
.
- References:
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