The dynamical problem for a non self-adjoint Hamiltonian

TL;DR

This paper reviews recent developments in quasi-hermitian quantum mechanics, focusing on quantum dynamics in Schrödinger and Heisenberg pictures and discussing the role of Krein spaces.

Contribution

It provides a comprehensive review of the dynamical aspects of non-self-adjoint Hamiltonians within quasi-hermitian quantum mechanics, highlighting the significance of Krein spaces.

Findings

Analysis of quantum dynamics in non-self-adjoint Hamiltonians

Discussion on the role of Krein spaces in quantum mechanics

Summary of recent advances in quasi-hermitian quantum theory

Abstract

We review some recent results of the so-called quasi-hermitian quantum mechanics, with particular focus on the quantum dynamics both in the Schr\"odinger and in the Heisenberg representations. The role of Krein spaces is also discussed.