Jost function

In scattering theory, the Jost function is the Wronskian of the regular solution and the (irregular) Jost solution to the differential equation ${\displaystyle -\psi ''+V\psi =k^{2}\psi }$. It was introduced by Res Jost.

We are looking for solutions ${\displaystyle \psi (k,r)}$ to the radial Schrödinger equation in the case ${\displaystyle \ell =0}$,

A regular solution ${\displaystyle \varphi (k,r)}$ is one that satisfies the boundary conditions,

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