Is an Electron a Wave? Understanding the Nature of Electrons

[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.

 

[haael]

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

 

[LSMOG]

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

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

 

[haael]

Yes, every particle is a quantum wave.

 

[bhobba]

Its not a wave - or anything classical. Its quantum stuff,.

Here is a much better way to view quantum stuff:
http://www.scottaaronson.com/democritus/lec9.html

What can sometimes be wavelike is the wave-function:
https://ocw.mit.edu/courses/physics...pring-2013/lecture-notes/MIT8_04S13_Lec03.pdf

Of course you can trust MIT.

Thanks
Bill

 

[bhobba]

Yes, every particle is a quantum wave.

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

Thanks
Bill

 

[haael]

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

 

[bhobba]

Rubbish, as I think has been pointed out to you l

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

 

[Demystifier]

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

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

 

[bhobba]

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

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

 

[haael]

Is the Dirac Delta Function a wave?

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

 

[bhobba]

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

It obeys the Schrödinger equation - I will leave those into classifying DE equations to comment if its wave or not (I don't 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

 

[Demystifier]

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

I was just kidding you.

Concerning the delta-function, it's nice to repeat that "wave" function is really a square-root of the delta-function:
https://www.physicsforums.com/threa...luding-dirac-delta.873711/page-2#post-5487662
https://www.physicsforums.com/threa...luding-dirac-delta.873711/page-2#post-5488516

 

[Demystifier]

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

It obeys the Schrödinger equation - I will leave those into classifying DE equations to comment if its wave or not (I don't 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.

1) In math literature on PDE's, Schrödinger 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 Schrödinger or wave equation must involve a dependence on time. Neither Schrödinger 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 Schrödinger equation:
https://arxiv.org/abs/quant-ph/0505143

 

[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!

 

[Demystifier]

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!

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.

 

[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.

 

[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.