On "non-Hermitian Quantum Mechanics"

TL;DR

This paper critically examines claims about non-Hermitian, PT-symmetric Hamiltonians in quantum mechanics, arguing that with the right inner product, such Hamiltonians are effectively Hermitian, questioning the novelty of these approaches.

Contribution

It clarifies that PT-symmetric Hamiltonians become Hermitian under suitable inner products, challenging the perceived novelty of non-Hermitian quantum mechanics approaches.

Findings

PT-symmetric Hamiltonians are Hermitian with an appropriate inner product

The supposed advantages of non-Hermitian Hamiltonians are redundant

The exercise of using non-Hermitian operators may be unnecessary

Abstract

A series of recent papers ``Faster than Hermitian Quantum Mechanics'' and related articles made a point of the possibility of a non-Hermitian, but PT-symmetric, operator to play the role of a Hamiltonian. In particular, they show that with an appropriate choice of an inner product, the evolution generated by such an operator will conserve the norm and scalar product. Here we observe that if one chooses such an inner product then the Hamiltonian in question is actually Hermitian, and the whole exercise is to a certain degree redundant.