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The derivative of the Floquet transform equals the Floquet tranform of the derivative. But can the Floquet tranform of the derivative of a function $f(r)$ can be expressed in terms of the Floquet tranform of the function $f(r)$? So, is there a relation between $(U \frac{\partial f}{\partial r})(r)$ and $(Uf)(r)$ (like there is for the Fourier transform, i.e. $(F \frac{\partial f}{\partial r})(r)=iω(Ff)(r)$? Many thanks in advance ! Jeff |
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wasn't this answered yesterday? http://mathoverflow.net/questions/64003/floquet-transform-of-the-derivative-of-a-function there is a relation, but it requires differentiation with respect to $r$; the parameter $k$ in the Floquet transform does not know how $f(r)$ varies within a unit cell of the lattice, so there is no analogue of the algebraic relation you have for the Fourier transform. |
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