phonons!

[nibot]

The energy of a lattice vibration is quantized. The quantum energy is called a phonon in analogy with the photon of the electromagnetic wave. Elastic waves in crystals are made up of phonons. Thermal vibrations in crystals are thermally excited phonons, like the thermally excited photons of black-body electromagnetic radiation in a cavity. The energy of an elastic mode of angular frequency ω is ε=(n+1/2)ℏω when the mode is occupied by n phonons.

Solid state physics is a lot more interesting than I'd thought! (Then they go on to talk about plasmons, magnons, polarons, and excitons...) Even planck's constant shows up!

Comments

[shamster.livejournal.com]

Shouldn't the angular quantum number (nu) be used instead of n? Or do you not care for nomenclatural preservation?

Also, what's the advantage in defining vibrations as phonons instead of just saying 'vibrations'. And... What's meant by a "thermal" vibration?

What's the special part about planck's const.?

[nibot.livejournal.com]

I've always seen quantum states indexed by n.

Phonons are more than vibrations precisely because they are quantized in energy in a way analagous to elementary particles and also because they act like particles, which is pretty outrageous at first glance. But I just started reading about them today, so I am not so sure about all the possible wonders of phonons.

Thermal vibrations... I assume that means that it's the inherent vibration described by temperature. (As opposed by outside impulse?)

Planck's constant is solidly a quantum mechanical thing, and to see it showing up in the vibrational modes of macroscopic solids is shocking. Well, kind of.

Well, I don't know much about it yet, but it seems like a very interesting way of describing things. Apparently quite useful too, since you can - apparently - start talking about "electron/phonon interactions" as if a phonon were a real particle.

[nibot.livejournal.com]

Also: Phonons of wavevector k will interact with particles such as photons, neutrons, and electrons as if it had a momentum hk/2π. In inelastic scattering, the phonon really behaves like a particle. I think this is because the atoms in the crystal act like simple harmonic oscillators, which in turn have quantized vibrational modes... but there's more to it.

[shamster.livejournal.com]

planck's constant shows up everywhere. I've seen it used in solid state before.

I suppose you're right about the n, it's the energy quantum number... the nu, which I meant to say 'l' is the angular momentum quantum number for elementary particles (read:electrons)