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

Abstract

A new formulation of unitary quantum mechanics is proposed. Conceptually our proposal is inspired not only by the conventional interaction picture (where the wave functions and the observables do both vary with time) and by the newer, non-Hermitian version of Schrödinger picture (where the Hamiltonians with real spectra are still stationary) but also by their universal non-Hermitian interaction-picture “overlap” (NIP) in which the physical inner-product metric in Hilbert space is also time-dependent. The main idea of the innovation (called “hybrid interaction picture”, HIP) lies in a partial simplification of the NIP Hilbert-space metric achieved via a partial preconditioning of the operators (in this sense we call their necessary Hermitization “hybrid”). Via an illustrative example it is shown that the HIP approach might open new ways towards the technically optimal quantum-model-building strategies.