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

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

2005-02-02

arxiv.org/abs/math-ph/0502009v2

J.Phys.A38:3665-3678,2005

Physics

Mathematical Physics

15 pages, 1 figure v2: minor conceptual changes

Scientific paper

10.1088/0305-4470/38/16/014

This paper presents an underlying analytical relationship between the $\mathcal{PT}$-pseudo-norm associated with the $\mathcal{PT}$-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 $\mathcal{PT}$-pseudo-norm, which has been observed as a generic feature of the $\mathcal{PT}$-inner product, is essentially controlled by the derivative of Stokes multiplier with respect to eigenparameter.

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