Thanks, DrDu, however I think that I found a way to explicitly see this periodicity. My problem was that I assumed
that free particle solution ##\psi_{\mathbf{k}} = A\exp(i\mathbf{k}\mathbf{r}) + A\exp(i\mathbf{k}\mathbf{r})##
is a special form of a Bloch wave and I couldn't see any periodicity...
Again, thanks for replies. However I still need to clear things up. Are theese points really correct?
Single bloch wave is not periodic in ##\mathbf{k}## space
However we can map solutions to 1st Briullin zone ##\psi_{\mathbf{k}'} = \psi_{\mathbf{k} + \mathbf{G}} = \psi_{\mathbf{k}, j}## by...
Thanks for reply.
So how to understand proposition, that every ##\mathbf{k}## can be mapped to first BZ. Can anyone give me practical example? There are many sources where relation ## \psi_{\mathbf{k}} = \psi_{\mathbf{k} + \mathbf{G}} ## is given.
How to understand that Bloch wave solutions can be completely characterized
by their behaviour in a single Brillouin zone? Given Bloch wave:
\begin{equation*}
\psi_{\mathbf{k}}(\mathbf{r}) = u_{\mathbf{k}}(\mathbf{r}) \exp (i\mathbf{k}\mathbf{r})
\end{equation*}
I can write wavefunction for...
It is all just a chain rule :)
\frac{1}{2}\partial_{\mu}\partial_{\nu}\frac{1}{l^{2}-\triangle+i\epsilon}=\partial_{\mu}\left[\frac{-l_{\nu}}{\left[l^{2}-\triangle+i\epsilon\right]^{2}}\right]...
Can anyone help me with the expansion of the integral
I_{\mu\nu}=\int d^{4}l\frac{4l_{\mu}l_{\nu}-g_{\mu\nu}l^2}{(l^{2}-B+i\epsilon)^{3}}.
I would like to know how it could be expanded into two terms
I_{\mu\nu}=\frac{1}{2}\int d^{4}l\frac{\partial^2}{\partial l^\mu \partial...
Good day to everyone. I am trying to apply dimensional regularization to divergent integral
\int\frac{d^{4}l}{\left(2\pi\right)^{4}}\frac{4\, l_{\mu}l_{\nu}}{\left[l^{2}-\triangle+i\epsilon\right]^{3}}.
I am very new to these thing. The first question is how should i apply Wicks rotation to...
No, the problem is that in degenerate perturbation theory we take the basis for our perturbed state function only the wave-functions of degenerate states from unperturbed system and skip others, which belong to nendegenerate states.
H0\phi0n=E0n\phi0n
Assume that we have r degenerate...
Why when we analyse time dependant perturbation theory, we take that the diagonal elements of matrix <i|W(t)|j> are equal to zero?
Why in degenerate perturbation theory we assume that perturbed wavefunctions of degenerate states can be expressed in the base of unperturbed wavefunctions of...
I can't get the variation of formula
http://img813.imageshack.us/img813/3754/38919739.png
in the form of
[PLAIN][PLAIN]http://img839.imageshack.us/img839/536/96608635.png.
Can anyone help me. Sorry, I am not good at math :)
At the moment i am reading Davydov A.S. Quantum mechanics book. And i need help to derive relation formula for multipole radiation
[PLAIN]http://img827.imageshack.us/img827/8974/formulal.png
Thank you in advance :)