# What is an “Interaction Hamiltonian”

I'm an undergraduate reading up on some quantum physics so that I can help out more in the lab that I'm working in this summer. In the book I'm reading (Shankar's "Principles of Quantum Mechanics") I just came across the term interaction Hamiltonian in describing how orbiting electrons interact with a magnetic field.

I have an idea of what it might mean, but I can't find a good explanation anywhere. What is an "interaction Hamiltonian", and how does it differ from a standard Hamiltonian?

$$H = \frac{p^2}{2m} + U -\boldsymbol \mu \cdot \mathbf E(t)$$ the term $$U$$ is potential energy, and $$-\boldsymbol \mu \cdot \mathbf E(t)$$ is interaction Hamiltonian, because $\mathbf E(t)$ describes electric field which is not being described by the Hamiltonian, but interacts with the system.
• If it does not depend on external variable (like external field), only on the variables of the system, I wouldn't call it interaction term, the same I would not call potential energy $U$ as interaction term, but I suppose others may do it differently. – Ján Lalinský Jun 18 '14 at 11:16
• Lalinsky: $U$ is the interaction because without it the kinetic terms sole describe a free motion. – Vladimir Kalitvianski Jun 18 '14 at 12:24