Commuting operators

[Niles]

Hi

Say I have the creation/annihilation operators for fermions given by c and the exponential operator exp(-iHt), where H denotes the Hamiltonian of the (unperturbed) system. Is there any way for me to find out if exp(-iHt) and c (and its adjoint) commute?

Best,
Niles.

[Careful]

Hi

Say I have the creation/annihilation operators for fermions given by c and the exponential operator exp(-iHt), where H denotes the Hamiltonian of the (unperturbed) system. Is there any way for me to find out if exp(-iHt) and c (and its adjoint) commute?

Best,
Niles.
They don't commute, H = k c*c and {c,c*} = 1, therefore [H, c] = - k c. You can work out the rest.