Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation

TL;DR

The paper introduces a new reformulation of quantum mechanics called the hybrid interaction picture (HIP), which simplifies the mathematical framework and offers potential for improved model-building in unitary quantum systems.

Contribution

It proposes the hybrid interaction picture (HIP), combining a simplified Hilbert-space metric with preconditioned observables, advancing the non-Hermitian interaction picture framework.

Findings

Demonstrates potential for new quantum model-building strategies

Simplifies the mathematical structure of non-Hermitian quantum mechanics

Provides an illustrative example of the formalism's application

Abstract

A reformulation of quantum mechanics called ``hybrid interaction picture'' (HIP) is proposed. In contrast to its current non-Hermitian-interaction-picture (NIP) predecessor the new formalism combines a simplification of the NIP Hilbert-space metric with an innovative preconditioning of the observables of interest. Via an illustrative example it is shown that the idea might open new ways towards optimal model-building strategies in quantum theory of unitary systems.