# Measure the speed of electron wave

1. Oct 19, 2005

### zbl1905

Measure the speed of electron wave
By theory of electron wave(E=hv=mcc,P=h/λ=mV),we can get the speed of electron wave
v=cc/V>c
but physicist consider it is not possible.I think it should proved by experiment.The follow experiment may gave us some new information.,Please look at picture
http://photo.163.com/openpic.php?user=zbl1905&pid=453581556&_dir=/18580977
There are three holes(A,B,C) in two boards(E F).,A switch is put in hole C.
electron wave transmit from left to right
1)At first ,the switch is closed.. Diffractive stripe will appear on board G,
2)At T1, ,the switch is opened.
3) At T2, diffractive stripe is changed.I don’t know what will happen.
4) speed of electron wave=L(CG)/(T2-T1).We can let L(CG) long enough to insure exact measure.

2. Oct 20, 2005

### vanesch

Staff Emeritus
This is the difference between the phase velocity and the signal or group velocity. You can do a computer simulation if you want to. The velocity you cite, v = c^2/V is the phase velocity. It is valid for each individual Fourier component, but as such, does not "propagate" anything, because a single Fourier component is present everywhere, at constant density. However, to simulate the "closure of the slit", you will have to introduce several Fourier components in your wave (to make up something that looks like a step function). Although each individual Fourier component will still rotate and "simulate" the phase velocity for each one, the movement of the "blob", or front of the step function will move at a totally different velocity: the group velocity.

Look up concepts such as "wave packet".
Or have a look at wikipedia: http://en.wikipedia.org/wiki/Phase_velocity and the links therein.

cheers,
Patrick.

3. Oct 20, 2005

### Hans de Vries

The phase speed $\frac{c^2}{v}$ is not the physical speed of the particle. There is a simularity
between classical phase speed and group speed but that's only part of the story.

If you want to understand the nature of the de Broglie wave then it's
mandatory to look at it with Special Relativity in mind. It actually becomes
quite simple then. A localized wave packet at rest does have the same phase
everywhere. If you look at it from a different reference frame then the phase
becomes $e^{ipx/\hbar}$, that is, The wave packet becomes modulated with a sinusoidal
function with a wave length depending on the speed. This phase then moves
again with a speed of $c^2/v$.

This is however the effect of the non-simultaneity of special relativity.
I've gone through some effort to explain these effects here:
http://www.chip-architect.com/physics/deBroglie.pdf
with images from computer simulations.

Regards, Hans

Last edited: Oct 20, 2005