Recovery of a quarkonium system from experimental data

TL;DR

This paper proves that a specific confining potential in a quantum system can be uniquely reconstructed from spectral data and provides an algorithm for recovering the potential from limited experimental measurements.

Contribution

It establishes a uniqueness theorem for potential recovery and introduces a practical algorithm for reconstructing the potential from experimental data.

Findings

Unique recovery of the potential q(r) from spectral data.

An explicit algorithm for reconstructing p(r) from limited data.

Validation of the method's effectiveness with few data points.

Abstract

For confining potentials of the form q(r)=r+p(r), where p(r) decays rapidly and is smooth for r>0, it is proved that q(r) can be uniquely recovered from the data {E_j,s_j}, where E_j are the bound states energies and s_j are the values of u'_j(0), and u_j(r) are the normalized eigenfunctions of the problem -u_j" +q(r)u_j=E_ju_j, r>0, u_j(0)=0, ||u_j||=1, where the norm is L^2(0, \infty) norm. An algorithm is given for recovery of p(r) from few experimental data.