Variational description of continuum states in terms of integral relations

TL;DR

This paper introduces a method using integral relations derived from the Kohn Variational Principle to describe continuum scattering states without needing explicit asymptotic wave function forms, simplifying phase-shift calculations.

Contribution

It presents a novel application of integral relations from the KVP that allows phase-shift computation from bound state wave functions and simplifies scattering analysis.

Findings

Phase-shifts can be obtained from bound state wave functions.

Integral relations work without explicit asymptotic wave functions.

Application to Hyperspherical Adiabatic method demonstrated.

Abstract

Two integral relations derived from the Kohn Variational Principle (KVP) are used for describing scattering states. In usual applications the KVP requires the explicit form of the asymptotic behavior of the scattering wave function. This is not the case when the integral relations are applied since, due to their short range nature, the only condition for the scattering wave function $\Psi$ is that it be the solution of $(H-E)\Psi=0$ in the internal region. Several examples are analyzed for the computation of phase-shifts from bound state type wave functions or, in the case of the scattering of charged particles, it is possible to obtain phase-shifts using free asymptotic conditions. As a final example we discuss the use of the integral relations in the case of the Hyperspherical Adiabatic method.