Reconstruction of full-space quantum Hamiltonian from its effective, energy-dependent model-space projection

TL;DR

This paper demonstrates that it is possible to reconstruct a full-space quantum Hamiltonian from an effective, energy-dependent model-space representation using algebraic methods, enabling better understanding of quantum systems.

Contribution

It introduces a method to reconstruct the full Hamiltonian from an effective model using matrix inversion and polynomial algebraic equations, which is a novel approach.

Findings

Reconstruction of the full Hamiltonian is feasible from effective models.

A linear algebraic operation (matrix inversion) is used to extract information.

Explicit solutions are provided for some simple cases.

Abstract

Reconstruction of a full-space quantum Hamiltonian from its effective Feshbach's model-space avatar is shown feasible. In a preparatory step the information carried by the effective Hamiltonian is compactified using a linear algebraic operation (matrix inversion). A ``universal'' coupled set of polynomial algebraic equations it then obtained. In a few simplest special cases their solution is given and discussed.