\begin{enumerate}
\item Write down the additional terms $H_{kin}'$ of the kinetic part
of the Hamiltonian.
- \item Chose a reasonable vector potential ${\bf A}$ to get a constant
+ \item Choose a reasonable vector potential ${\bf A}$ to get a constant
magnetic field ${\bf B}$ in $z$-direction.
\item Rewrite the Hamiltonian
using the definition of the angular momentum operator
\item Calculate the magnetic suscebtibility in a state $\phi$.
What term is responsible for the diamagnetic contribution?
{\bf Hint:} The magnetic suscebtibility is defined as
- $\chi=-\frac{1}{V}\frac{\partial^2 E}{\partial B^2}$.
+ $\chi=-\frac{1}{V}\mu_0\frac{\partial^2 E}{\partial B^2}$.
\item Assuming a spherically symmetric charge distribution the equality
$<\phi|x^2|\phi>=<\phi|y^2|\phi>=\frac{1}{3}<\phi|r^2|\phi>$
is valid. Rewrite the diamagnetic part of the suscebtibility