Abstract: We intend to recall that several familiar objects in applied and mathematical physics, such as, Jost functions, Floquet discriminants, and Evans functions, are actually (modified) Fredholm determinants associated with appropriate Birman-Schwinger-type integral operators.
In addition, we will describe multi-dimensional variations on a theme of Pais and Jost and their applicability to two- and three-dimensional Schrödinger operators. This topic revolves around modified Fredholm determinants, the Birman–Schwinger principle, and operator-valued Weyl–Titchmarsh functions (i.e., Dirichlet to Neumann maps), etc.