  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 $H^\dagger = H$ 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.
