I am trying to solve a problem of 1D electron system.
Given [tex]a,a^\dagger,b,b^\dagger[/tex] annihilation and creation operator which satisfy the fermion commutation relations diagonalize the following hamiltonian:
where [tex]v_F,\Delta[/tex] are c-numbers.
Prove that the spectrum is given by:
2. The attempt at a solution
I try to define the following operators (that form an su(2) algebra):
and to calculate the adjoint action but I don't know how to continue.
Please help me, thank you.