Stable minimum principles for scattering states

TL;DR

This paper introduces stable minimum principles for quantum scattering states that enable rigorous bounds on scattering amplitudes and are suitable for numerical computation, even with complex interactions.

Contribution

It presents a new family of stable minimum principles for scattering states, applicable to various potentials and interactions, improving numerical stability and accuracy.

Findings

States satisfying the minimum principles closely approximate true scattering states.

The principles provide rigorous bounds on scattering amplitudes.

Applicable to momentum-dependent, Coulomb, and inelastic scattering scenarios.

Abstract

Quantum-mechanical scattering states are energy eigenstates obeying particular boundary conditions, whose behavior at infinity encodes the S-matrix which defines the outcoming of scattering experiments. With an eye toward numerical algorithms for computing nonrelativistic S-matrices, we present a family of stable minimum principles for scattering states. States that approximately satisfy these minimum principles are shown to have a bounded difference with the true scattering states. These minimum principles and stability estimates can be used to obtain rigorous bounds on scattering amplitudes. We show that these minimum principles are applicable to momentum-dependent potentials, long-range (Coulomb) interactions, and elastic or inelastic scattering of bound states.