Energy levels

[jeheron]

In what materials/states of matter do energy bands form? What determines whether an energy band will exist? For example, do energy bands ever form in gases?

 

Cheers!

[timo]

Perhaps you shouldn´t over-interpret the energy bands. From a more abstract point of view they are merely a nice way to describe the possible energy levels for electrons in a periodic potential - but a very practical one for describing certain effects nonetheless.

Determining the energy eigenstates for multi-particle systems is a problem with an awesome complexity and can, in practice, only be done with very strong simplifications. In the case of the energy bands, the simplification used is that the electrons are in a static periodic potential and do not interact with each other (more sophisitcated models might include electron-electron interaction and slight deviations periodicity staticity, though). These conditions are quite well fulfilled by single-crystals and, given that the model still works, also sufficiently for polycrystals. Both, single- and polycrystals are solid states. It seems unlikely (to say the least) that periodicity of the ions is sufficiently satisfied in a fluid or a gas (I would spontaneously expect the energy-eigenstates to be bound to a single ion rather than being spread out over the whole crystal). Since the conditions are very different, I´d expect the resulting distribution of the energies not to be band-like.

Ok that was mostly just speculation from my side and I should note that I´m not a solid-state physicist. I mostly responded because to my knowledge no one else on this forum (at least no one that posted here during last year) is, either. But I hope it still helps you a bit.

 

Two questions from my side:

1) Why are you interested in energy-bands? While it´s refreshing to see that people can ask questions about something else than quantum gravity it´s a bit surprising for me that you do.

2) What´s your background on QM? I think energy-bands belong to the part of solid-state physics that, at least from the theoretical side, can only be understood from a QM perspective.

[jeheron]

1) I am completing my last year of secondary school in Australia, and energy bands are included in the course syllabus. This however is not my only motivation for asking the question I have. My passion is for physics, and to me, this is very interesting.

 

2) I have read a lot of superficial material that discusses QM, but nothing to deep. So my knowledge is limited. I am always looking to learn more though. In regards to this topic, I have read into the Pauli exclusion principle, and energy levels, in an attempt to understand energy bands.

[swansont]

Just guessing, but I suspect you get bands only when there is long-range order, since you have to have the electrons in a single system. So the only gas banding I'd expect is in a cold Fermi gas condensate, which has long-range order.