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Results tagged with condensed-matter
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user 251599
The study of physical properties of condensed phases of matter, including solids and liquids.
1
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The uniqueness of primitive vectors in a Bravais lattice
I am reading Chapter 4 of Ashcroft and Mermin (A&M) in which the basic definitions of a Bravais lattice (BL) -- as considered as a purely mathematical entity -- are being laid down. One of the definit …
- 1,261
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4
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What is Bloch's theorem really saying (isomorphism between Bloch eigenbasis and $k$-space)?
(Throughout this development, I neglect spin.)
Bloch's theorem, strictly speaking (according to Ashcroft and Mermin), says that given a (one-electron) Hamiltonian
$$\hat{H} = \frac{\hat{\mathbf{P}}^2} …
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3
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3
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Translating Ashcroft and Mermin's "Second Proof" of Bloch's Theorem to Dirac's Notation
At the end of this post I attach Ashcroft and Mermin's proof of Bloch's theorem which is not essential per se (the proof using lattice symmetries is more general), but is key in being used later as a …
- 1,261
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2
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Double counting and Pauli Exclusion in the semiclassical model of electron dynamics
In the end, I think this question is related to this one (which was never satisfactorily answered), but I extend slightly and therefore am asking a new question.
In discussing the semiclassical model …
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Why is the time evolution of occupied and unoccupied levels in a band under the influence of...
You may consider the following argument which freely accepts that the semiclassical equations of motion only apply to electrons. All this argument requires is that you also accept (as it seems you hav …
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On Bloch's Theorem and the standard Fourier proof
I am reading Ashcroft and Mermin and I am unfortunately finding the (standard) proof of Bloch's theorem presented there rather befuddling. The proof in its entirety is at the bottom of this post. I ha …
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