B Is an electron a wave?

1. Oct 14, 2016

LSMOG

Hallow, if we say electron is a wave, do we mean it oscillates up and down as is moves through space? I am lost please.

2. Oct 14, 2016

haael

Electron is a quantum wave. What is oscillating is its quantum phase, not posision.

3. Oct 14, 2016

LSMOG

Thanks Haael. Is this also the same for a photon, or all particles in general?

Last edited by a moderator: Oct 14, 2016
4. Oct 14, 2016

haael

Yes, every particle is a quantum wave.

5. Oct 15, 2016

Staff: Mentor

6. Oct 15, 2016

Staff: Mentor

Rubbish, as I think has been pointed out to you innumerable times,

Thanks
Bill

7. Oct 18, 2016

haael

Pointed out to me innumerable times? You must be confusing me with someone.

8. Oct 18, 2016

Staff: Mentor

Fair enough and I apologise. I had you confused.

But, and this is VERY importat - it is NOT a wave. I will repeat it to be clear - it is NOT a wave.

Sometimes, and not often, it has wavelike solutions - that's all.

Thanks
Bill

9. Oct 18, 2016

Demystifier

By "it", do you mean the wave function of the electron?

10. Oct 18, 2016

Staff: Mentor

Is the Dirac Delta Function a wave?

But you know the detailed answer as well as I do:
https://arxiv.org/pdf/quant-ph/0609163v2.pdf

To the OP, and others touting the wave view, please read the above.

Thanks
Bill

11. Oct 18, 2016

haael

If it obeys a wave equation, then I would call it a wave.

12. Oct 18, 2016

Staff: Mentor

It obeys the Schrodinger equation - I will leave those into classifying DE equations to comment if its wave or not (I dont think it is but its been a while since I studied PDE's) - but only in the position basis could the question even be asked.

I need to add its a minefield of some very advanced and complicated math:

Thanks
Bill

13. Oct 18, 2016

Demystifier

14. Oct 18, 2016

Demystifier

1) In math literature on PDE's, Schrodinger equation is not classified as "wave equation".
https://en.wikipedia.org/wiki/Wave_equation
For a brief recapitulation of all most important PDE's I highly recommend
https://people.maths.ox.ac.uk/trefethen/pdectb.html

2) A solution of Schrodinger or wave equation must involve a dependence on time. Neither Schrodinger equation nor wave equation involves a time-dependent delta-function as a solution.

3) Both equations can have a delta-function as an initial condition.

4) A time-dependent delta-function (i.e. a perfectly localized soliton) is a solution of the non-linear classical Schrodinger equation:
https://arxiv.org/abs/quant-ph/0505143

Last edited: Oct 18, 2016
15. Oct 18, 2016

vanhees71

The $\delta$ distribution (NOT function) is not a square-integrable function and thus doesn't represent a proper (pure) state of the electron. Don't confuse beginners with such imprecisions about the formalism! Also "plane-wave" solutions (momentum eigensolutions) don't represent proper pure states of the electron!

16. Oct 18, 2016

Demystifier

You are right that beginners should not be confused with these technicalities. But note that my $\delta_{\epsilon}(x)$ in the second link in #13 is a function, and that $\sqrt{\delta_{\epsilon}(x)}$ is a square-integrable function.

17. Oct 18, 2016

newjerseyrunner

The wave in quantum mechanics isn't like a wave in water or space or anything else you can imagine. The electron itself is a point particle, whose position is describes as a probability distribution that takes on a wave form. It can be thought of as in every possible position in the distribution at once and also none of them, finally choosing a definite position when it interacts with something else.

18. Oct 19, 2016

houlahound

Took me some time to be happy to just call things solutions to specific well defined problems.

The common dilemma of trying to get quantum objects to fit classical concepts just fades.