so i am looking into Landau Diamagnetism and am reading Dupre's paper. I am slightly confused at where he has got a term in his value of E from.
He states that:
$$ E=(n+1/2)\hbar\omega+\hbar^2k_z^2/2m $$
and i can easily get to the first part, but am confused where the second term $\hbar^2k_z^2...$ comes from as it always seems to disappear.
the hamiltonian i am using is
$$ H=(-\hbar^2/2m)*d^2/dy^2+\hbar^2k_z^2/2m+m\omega_c/2(y-\hbar k_x/m\omega_c) $$
however i may have the wrong indices (it could be $k_x$ or $k_z$ switched im not certain)