 Jost function

For radial quantum scattering, the incoming coefficient of the regular solution defines the Jost function, with convention $S(k)=F(-k)/F(k)$. A zero at $k=i\kappa$, $\kappa >0$, removes the exponentially growing component and produces a bound state, subject to regularity and normalizability. Poles of the outgoing numerator alone need not produce bound states.

The Jost function is a mathematical concept used primarily in quantum mechanics, particularly in the analysis of one-dimensional scattering problems. It arises in the context of solving the Schrödinger equation for a potential, and is particularly important for understanding the properties of scattering states and bound states in a quantum system. In more detail, the Jost function is associated with the solutions of the radial or one-dimensional Schrödinger equation, which can be expressed in terms of a potential.