Computing resonances with the Complex Absorbing Potential Method

Plamen Stefanov

We study the Schrodinger equation (other models are possible) in the whole
space with a potential localized in some compact region K. Outside K, the
dynamics is "free", so in  numerical computations, we should work in in some
bounded neighborhood of K. One way to "model infinity" is to add a complex
absorbing potential (CAP) -iW(x), where W is a non-negative potential with
support outside K. This is a widely used method in the Quantum Chemistry
Community, for example. We will present some estimates that show that the so
modified CAP Hamiltonian has eigenvalues that approximate very well the
resonances of the original problem. We will discuss some open questions and
some numerical results obtained so far by other people.