Is PT-symmetric quantum mechanics just quantum mechanics in a non-orthogonal basis?

Abstract

One of the postulates of quantum mechanics is that the Hamiltonian is Hermitian, as this guarantees that the eigenvalues are real. Recently there has been an interest in asking if $H^{†}=H$ is a necessary condition, and has lead to the development of PT-symmetric quantum mechanics. This note shows that any finite physically acceptable non-Hermitian Hamiltonian is equivalent to doing ordinary quantum mechanics in a non-orthogonal basis. In particular, this means that there is no experimental distinction between PT-symmetric quantum mechanics and ordinary quantum mechanics for finite systems. In particular, the claim that PT-symmetric quantum mechanics allows for faster evolution than Hermitian quantum mechanics is shown to be a problem of physical interpretation.

16 pages; references added, sign error fixed

References in corpus (8)

• Introduction to PT-Symmetric Quantum Theory
• Faster than Hermitian Quantum Mechanics
• Quantum Brachistochrone
• Scalar Quantum Field Theory with Cubic Interaction
• PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics
• Finite-Dimensional PT-Symmetric Hamiltonians
• A Critique of PT-Symmetric Quantum Mechanics
• Comment on ``PT-Symmetric versus Hermitian Formulations of Quantum Mechanics [hep-th/0511229]''

Cited by in corpus (3)

• Conceptual Problems in Scattering from Localized non-Hermitian Potentials
• Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution
• Faster than Hermitian Time Evolution