Second quantized hamiltonian change basis

[gonadas91]

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

 

[strangerep]

\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

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 $H_0$?

 

[gonadas91]

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!