I am reading quantum mechanics (Messiah) now. And I get confused about the condition for the validity of the sudden approximation in CH. XVII. The author use perturbation theory to derive the result
T<<\hbar/\delta \overline{H}
,when the Hamiltonian change over time T. The condition tells...
If I write down the transformation
a_p^{\dagger}=u_p\alpha_p^{\dagger}-v_p\alpha_{-p}
a^{\dagger} is the field operator after the transformation. Assume the ground state is
|g\rangle
a_p^{\dagger}|g\rangle=u_p\alpha_p^{\dagger}|g\rangle-v_p\alpha_{-p}|g\rangle
p is momentum. Do you mean...
I am reading the paper of one dimensional fermion system(Voits,1994,One dimensional fermi liquid, on p.998). In the paper, he use it to diagonalize the Hamiltonian. I know how Bogoliubov transformation canceled the cross term, but I cannot imagine the meaning of it. In quantum mechanics for one...
http://en.wikipedia.org/wiki/Bogoliubov_transformation
I try to know more about Bogoliubov transformation. I try to find some material to help me understand the transformation more. Most of the material I found are lack of physical explanation for me. Most of the many-body textbook(Fetter and...
I try to find the solution of the integrals below for more than a week.
\int_{p>0}^{\infty}\frac{\exp[-ap]}{p}dp
can anyone give me a hint about how to solve it?
Yes, I copy the definition from J.Voits onedimensional fermi liquid p.1008
I try to start from the density operator \rho(q)=\sum_k c_{k-q}^{\dagger}c_k.
Then, decompose the Fermion operatorc_k=\Theta(k)c_{R,k}+\Theta(-k)c_{L,k}.
Insert the relation into the density operator and expand it, I...
In one dimensional electron gas in charge density wave phase, as I know , the density of electrons will be periodic. The order parameter of charge density wave is written as
O_{CDW}(x)=\sum_s\psi_{L,s}^{\dagger}(x)\psi_{R,s}(x)
For Luttinger model, the \psi is the Fermion annihilation field...