0
votes
1answer
116 views

Overview and doubts about Bloch's theorem and the concept of partial density of states

So I have a large confusion with QM as applied to solid state. The following is a summary of what I know, what I think I know, and what I know I don't know. I hope to stir a discussion that will help ...
3
votes
1answer
132 views

Why does total spin conservation law forbid the spin wave gap in Heisenberg magnets?

What is the explanation for total spin conservation forbidding the spin wave gap in Heisenberg magnets?
1
vote
2answers
171 views

Eigenfunctions in periodic potential

For Hamiltonian $\operatorname H$ and lattice translation operator $\operatorname T$, if $$\operatorname H\psi=E\psi, \qquad \operatorname T\psi=e^{ik\cdot R}\psi,$$ and $$\operatorname ...
1
vote
0answers
40 views

Residual symmetries of the superposition of two fcc lattices

Fcc lattices are Bravais lattices and so are invariant under a set of discrete translations plus inversions over the 3 axis ($x\rightarrow -x$,$y\rightarrow -y$,$z\rightarrow -z$). When one superposes ...
3
votes
1answer
282 views

Lorentz invariance of a frequency- and wavelength- dependent dielectric tensor

Suppose we have a material described by a dielectric tensor $\bar{\epsilon}$. In frequency domain, this tensor depends on the wave frequency $\omega$ and the wave vector $\vec{k}$. Clearly not all ...
2
votes
3answers
350 views

About symmetry, and about electron density in crystals in particular

The book Introduction to Solid State Physics by Kittel says: "We have seen that a crystal is invariant under any translation of the form T [...]. Any local physical property of the crystal, such as ...