Second quantized hamiltonian change basis

1. Sep 23, 2015

Hello everyone, I m currently working on a problem that is freaking me out a bit, suppose I have a second quantized hamiltonian:

\begin{eqnarray}
H=H_{0}+ \epsilon d^{\dagger}d + V(d{\dagger}c_{0} + h.c)
\end{eqnarray}
In terms of some new operators, I would like to rotate the hamiltonian, so that one part of it is diagonalised in the new operators, how can I do this¿ And compute the matrix elements

2. Sep 28, 2015

Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Sep 28, 2015

strangerep

A bit more context in your question would help. (I actually started a reply when you first posted, but abandoned it because I was too short of time to guess your context.)

I'm guessing your d's are creation/annihilation operators satisfying canonical commutation relations(?). What is $c_0$? Is there an explicit expression for $H_0$?

4. Sep 29, 2015

Okei thanks for the reply! H0 represents a bath of conduction electrons, $d^{\dagger}$ and $d$ are fermionic operators on a impurity level, and c0 the fermionic operators at the edge of the conduction band. Its a non-interacting Anderson model. However, I could do it at the end so no help is needed, than you anyway!!