Pseudo-Hermitian Description of PT-Symmetric Systems Defined on a Complex Contour
| dc.creator | Mostafazadeh, Ali | |
| dc.date | 2004-10-01 | |
| dc.date | 2005-02-18 | |
| dc.date.accessioned | 2026-07-07T06:11:00Z | |
| dc.date.available | 2026-07-07T06:11:00Z | |
| dc.description | We describe a method that allows for a practical application of the theory of pseudo-Hermitian operators to PT-symmetric systems defined on a complex contour. We apply this method to study the Hamiltonians $H=p^2+x^2(ix)^ν$ with $ν\in(-2,\infty)$ that are defined along the corresponding anti-Stokes lines. In particular, we reveal the intrinsic non-Hermiticity of $H$ for the cases that $ν$ is an even integer, so that $H=p^2\pm x^{2+ν}$, and give a proof of the discreteness of the spectrum of $H$ for all $ν\in(-2,\infty)$. Furthermore, we study the consequences of defining a square-well Hamiltonian on a wedge-shaped complex contour. This yields a PT-symmetric system with a finite number of real eigenvalues. We present a comprehensive analysis of this system within the framework of pseudo-Hermitian quantum mechanics. We also outline a direct pseudo-Hermitian treatment of PT-symmetric systems defined on a complex contour which clarifies the underlying mathematical structure of the formulation of PT-symmetric quantum mechanics based on the charge-conjugation operator. Our results provide a conclusive evidence that pseudo-Hermitian quantum mechanics provides a complete description of general PT-symmetric systems regardless of whether they are defined along the real line or a complex contour. | |
| dc.description | 28 pages, 1 figure, revised version, to appear in J. Phys. A | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0410012 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0410012 | |
| dc.identifier | J.Phys. A38 (2005) 3213-3234 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/92413 | |
| dc.subject | Quantum Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | Pseudo-Hermitian Description of PT-Symmetric Systems Defined on a Complex Contour | |
| dc.type | text |