A class of inverse problems in physics

Abstract

If physics students are exposed at all to inverse problems, it is usually in the context of specialized treatments of quantum scattering processes. Inverse problems are, however, important in a wide variety of applications, such as gravitational lensing, seismological exploration, and underwater acoustic tomography. Students can be introduced to inverse problems in undergraduate courses in mechanics, optics, and quantum mechanics. This paper presents some simple examples whose solution in each case involves Abel’s integral equation, illustrating the ubiquity of this mathematical relation in diverse areas of physics.