Remarks on PT-pseudo-norm in PT-symmetric quantum mechanics

Abstract

This paper presents an underlying analytical relationship between the $\mathcal{P}\mathcal{T}$-pseudo-norm associated with the $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian $H=p^2+V(q)$ and the Stokes multiplier of the differential equation corresponding to this Hamiltonian. We show that the sign alternation of $\mathcal{P}\mathcal{T}$-pseudo-norm, which has been observed as a generic feature of the $\mathcal{P}\mathcal{T}$-inner product, is essentially controlled by the derivative of Stokes multiplier with respect to eigenparameter.

15 pages, 1 figure v2: minor conceptual changes

References in corpus (1)

• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics

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