Electrons in Metal: Wave-Particle Duality

[Karim Habashy]

Hi All,

Lets assume, we have piece of cubic copper of side length 1 cm metal with neutral charge, so:

1) The free electrons in this piece of copper exist everywhere as waves? , each electron with its quantum state.
2) On applying an external electric field the wave-function collapse and they start behaving like particles ?

Are the above conclusions right ?

Thanks

 

[mfb]

1) The free electrons in this piece of copper exist everywhere as waves? , each electron with its quantum state.

It is just a model, but that model is not so bad here.

2) On applying an external electric field the wave-function collapse and they start behaving like particles ?

No. Unless your "electric field" is something like visible light, with sufficient energy to excite electrons.

 

[Karim Habashy]

It is just a model, but that model is not so bad here.

Is there a more accurate model ?

No. Unless your "electric field" is something like visible light, with sufficient energy to excite electrons.

But how can we account for the drift velocity, due to electrons migration by applying an electric field

 

[DrDu]

There are electronic wavefunctions for drifting electrons.

 

[Karim Habashy]

There are electronic wavefunctions for drifting electrons.

You mean the electrons behaving as wave packets of plane waves ? , if so, its interesting how a field affects a wave packet.
Can we say an electron is a particle in reaction and a wave in action ?

 

[mfb]

Is there a more accurate model ?

Depends on what you want to do.

But how can we account for the drift velocity, due to electrons migration by applying an electric field

A wavefunction can have a momentum, corresponding to drifting electrons.

Can we say an electron is a particle in reaction and a wave in action ?

Forget the whole idea of "wave or particle". An electron is neither. It is a quantum object.

 

[my2cts]

What is your goal? To interpret quantum mechanics? To understand a metal ?

 

[Karim Habashy]

What is your goal? To interpret quantum mechanics? To understand a metal ?

Neither, I am just trying to comprehend, how electrons (quantum particles) exist everywhere in the metal and in the same time obeys Newtons laws of motion under the application of an electric field.

 

[ZapperZ]

You can describe electron motion and charge transport in metals using full quantum mechanical description via the Kubo formulation. But why would you want to if the characteristics that you want to measure can be described sufficiently by the semi-classical Boltzmann transport description? To want to use the full QM picture (which isn't easy at all) to get at those characteristics is like asking a house builder to use Special Relativity to do his job!

Zz.