Inverse spectrum problem for quasi-stationary states

Understand

In this work we present a semi-classical approach to solve the inverse spectrum problem for one-dimensional wave equations for a specific class of potentials that admits quasi-stationary states.

• We show how inverse methods for potential wells and potential barriers can be generalized to reconstruct significant parts for the combined potentials.
• For the reconstruction one assumes the knowledge of the complex valued spectrum and uses the exponential smallness of its imaginary part.
• Analytic spectra are studied and a recent application of the method in the literature for gravitational wave physics is discussed.