The Intrinsic Exceptional Point: A Challenge in Quantum Theory

Abstract

In spite of its unbroken PT symmetry, the popular imaginary cubic oscillator Hamiltonian 𝐻(𝐼𝐶)=𝑝2+i𝑥3 does not satisfy all of the necessary postulates of quantum mechanics. This failure is due to the “intrinsic exceptional point” (IEP) features of 𝐻(𝐼𝐶) and, in particular, to the phenomenon of a high-energy asymptotic parallelization of its bound-state-mimicking eigenvectors. In this paper, it is argued that the operator 𝐻(𝐼𝐶) (and the like) can only be interpreted as a manifestly unphysical, singular IEP limit of a hypothetical one-parametric family of certain standard quantum Hamiltonians. For explanation, ample use is made of perturbation theory and of multiple analogies between IEPs and conventional Kato’s exceptional points.