Do wave-packets of Blochwaves spread over time?

[Abigale]

Hi,
to describe electronic transport and for example bloch oscillations, one uses a wave-packet build of bloch waves (with a band index n and an effective mass m*).

Do these wave-packets of blochwaves also spread (disperse) over time?

 

[fluidistic]

Hi,
to describe electronic transport and for example bloch oscillations, one uses a wave-packet build of bloch waves (with a band index n and an effective mass m*).

Do these wave-packets of blochwaves also spread (disperse) over time?

Could you please give a reference? My limited experience so far has been different. I always assumed each individual electron was in an eigenstate of the Hamiltonian operator at all times, and as such its wavefunction was never a superposition of eigenstates (or a wave-packet). I have never seen a wavepacket made of Bloch oscillations so far, but I'd really be interested in knowning the answer to your question, so please give some reference that I can look up.

 

[Abigale]

Hi sure,

in Ashcroft Mermin "Solid State Physics".
Chapter 12 "Description of the Semiclassical Model" deals with the description of electrons by wave packets of Bloch Electrons.

Would be nice if you could explain me if it also spreads...

 

[fluidistic]

Hi sure,

in Ashcroft Mermin "Solid State Physics".
Chapter 12 "Description of the Semiclassical Model" deals with the description of electrons by wave packets of Bloch Electrons.

Would be nice if you could explain me if it also spreads...

Thanks, at a first quick glance my guess is that the case is no different than the case of a free particle. I.e. there should be a spread of the wavefunction with time.
Nevertheless, it seems possible to use some tricks to prevent the spreading of the wavefunction (described there: http://www.itp.ac.cn/~suncp/papers/PR/PRA06-3.pdf) by using a magnetic field and considering a zero momentum Gaussian wave packet.

 

[ZapperZ]

Hi,
to describe electronic transport and for example bloch oscillations, one uses a wave-packet build of bloch waves (with a band index n and an effective mass m*).

Do these wave-packets of blochwaves also spread (disperse) over time?

It doesn't.

First of all, think of what happens if it does. It means that your conductor will be behaving differently 2 seconds later when you measure its properties, because the charge carriers have "disperses" over time.

The Bloch wave functions are analogous to standing waves. It is the wavefunction for the entire solid, because you are imposing a repeated/periodic boundary condition over the entire space. It is also why there are gaps in the band, because the states representing those wavefunction cannot be sustained by the boundary conditions.

Zz.

 

[DrDu]

Free electrons are a special case of Bloch electrons. Hence, in general, Bloch wave packets do disperse.

 

[fluidistic]

The Bloch wave functions are analogous to standing waves. It is the wavefunction for the entire solid, because you are imposing a repeated/periodic boundary condition over the entire space.

I am not the OP, but I'd like to make sure I am understanding your sentence correctly. A single Bloch wavefunction represents the wavefunction of a single electron, right? By entire solid you mean that this wavefunction extends over the whole solid, not that it represents the wavefunction of all the electrons in that solid, right?