# Homework Help: Time independent perturbation theory

1. Jan 22, 2009

### ice109

1. The problem statement, all variables and given/known data

Assume that H0 describes a paramagnetic system that couples to a magnetic field via
the Zeeman effect, i.e. V = −μB, where μ is the magnetic moment. Note that for the
unperturbed paramagnetic system the probability of having an up-spin is equal to that for
a down-spin. Show that the magnetic susceptibility, defined as E = EGS −$\frac{1}{2}\chi B^2$, where
EGS is the ground state energy in the absence of field, is always non-negative. Write down
the expression for the susceptibility.
Note: A similar expression for a susceptibility is valid for an arbitrary perturbation. This
is known as the Lehmann representation applied to the linear response of the system to
the perturbation.

2. Relevant equations

3. The attempt at a solution

i have no idea what's being asked here? is the perturbation −μB to a free particle hamiltonian?

Last edited: Jan 22, 2009