Title: PT-Symmetry & Non-Hermitian Quantum Mechanics
Abstract: In quantum mechanics (QM), hermiticity has traditionally been taken as a requirement in order to ensure that operators associated with observables have real eigenvalues but also to ensure that the time-evolution is unitary. In my talk, I will introduce the notion of parity-time (PT) symmetry and show how it ensures real eigenvalues. Moreover, I will discuss a set of postulates for non-Hermitian QM and how they generalize from the Dirac-von Neumann postulates of Hermitian QM. Especially how the pre-assigned Dirac norm of Hermitian QM must be abandoned in favor of a dynamically determined norm and how PT-symmetry is a necessary and sufficient condition for unitary time-evolution.