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.

arXiv comment15 pages, 1 figure v2: minor conceptual changes

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• Pseudo-Hermiticity and some consequences of a generalized quantum condition
• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
• PT-Symmetric Quantum Theory Defined in a Krein Space
• General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space
• Spiked potentials and quantum toboggans
• PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
• Quasi-exactly solvable quartic: elementary integrals and asymptotics
• Classification of the conditionally observable spectra exhibiting central symmetry
• A Bound on the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential