The physical interpretation of non-Hermitian Hamiltonians and other observables

Abstract

A recent surge of publications about non-Hermitian Hamiltonians has led to considerable controversy and — in our opinion — to some misunderstandings of basic quantum mechanics. The present paper scrutinizes the metric associated with a quasi-Hermitian Hamiltonian and its physical implications. The consequences of the non-uniqueness such as the question of the probability interpretation and the possible and forbidden choices of additional observables are investigated and exemplified by specific illustrative examples. In particular, it is argued that the improper identification of observables lies at the origin of the claimed violation of the brachistchrone transition time between orthogonal states. The need for further physical input to remove ambiguities is pointed out.PACS Nos.: 03.65.–w, 03.65.Ca, 03.65.Ta, 03.65.Xp