Calculation of the metric in the Hilbert space of a PT -symmetric model via the spectral theorem

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 24, 2008, Pages

  Krejiík, David ^a  

^a NUCLEAR PHYSICS INSTITUTE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 48249145437     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/24/244012     Document Type: Article

References (25)

1. Krejiík D, Bíla H and Znojil M 2006 Closed formula for the metric in the Hilbert space of a -symmetric model J. Phys. A: Math. Gen. 39 10143-53
2. Cycon H L, Froese R G, Kirsch W and Simon B 1987 Schrödinger Operators, with Application to Quantum Mechanics and Global Geometry (Berlin: Springer)
3. Joye A, Kunz H and Ch Ed Pfister 1991 Exponential decay and geometric aspect of transition probabilities in the adiabatic limit Ann. Phys. 208 299-332
4. Davies E B 2002 Non-self-adjoint differential operators Bull. London Math. Soc. 34 513-32
5. Bender C M and Boettcher P N 1998 Real spectra in non-Hermitian Hamiltonians having symmetry Phys. Rev. Lett. 80 5243-6
6. Bender C M 2007 Making sense of non-Hermitian Hamiltonians Rep. Prog. Phys. 70 947-1018
7. Scholtz F G, Geyer H B and Hahne F J W 1992 Quasi-Hermitian operators in quantum mechanics and the variational principle Ann. Phys. 213 74-101
8. Mostafazadeh A 2002 Pseudo-Hermiticity versus PT symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian J. Math. Phys. 43 205-14
9. Mostafazadeh A 2002 Pseudo-Hermiticity versus PT symmetry: II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum J. Math. Phys. 43 2814-6
10. Mostafazadeh A 2002 Pseudo-Hermiticity versus PT symmetry: III. Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries J. Math. Phys. 43 3944-51
11. Swanson M S 2004 Transition elements for a non-Hermitian quadratic Hamiltonian J. Math. Phys. 45 585-601
12. Geyer H B, Scholtz F G and Snyman I 2004 Quasi-hermiticity and the role of a metric in some boson Hamiltonians Czech. J. Phys. 54 1069-73
13. Jones H F 2005 On pseudo-Hermitian Hamiltonians and their Hermitian counterparts J. Phys. A 38 1741-6
14. Mostafazadeh A 2006 Metric operator in pseudo-Hermitian quantum mechanics and the imaginary cubic potential J. Phys. A 39 10171-88
15. Mostafazadeh A 2006 Delta-function potential with a complex coupling J. Phys. A 39 13495-506
16. Mostafazadeh A 2006 Differential realization of pseudo-hermiticity: a quantum mechanical analog of Einstein's field equation J. Math. Phys. 47 072103
17. Scholtz F G and Geyer H B 2006 Operator equations and Moyal products-metrics in quasi-Hermitian quantum mechanics Phys. Lett. B 634 84-92
18. Scholtz F G and Geyer H B 2006 Moyal products-a new perspective on quasi-hermitian quantum mechanics J. Phys. A 39 10189-205
19. Figueira de Morisson Faria C and Fring A 2006 Isospectral Hamiltonians from Moyal Products Czech. J. Phys. 56 899-908
20. Musumbu D P, Scholtz F G and Geyer H B 2007 Choice of a metric for the non-hermitian oscillator J. Phys. A 40 F75-80
21. Kretschmer R and Szymanowski L 2004 Quasi-Hermiticity in infinite-dimensional Hilbert spaces Phys. Lett. A 325 112-7
22. Albeverio S, Fei S M and Kurasov P 2002 Point interactions -Hermiticity and reality of the spectrum Lett. Math. Phys. 59 227-42
23. Kato T 1966 Perturbation Theory for Linear Operators (Berlin: Springer)
24. Adams R A 1975 Sobolev Spaces (New York: Academic)
25. Kaiser H Ch, Neidhardt H and Rehberg J 2003 On one dimensional dissipative Schrödinger-type operators their dilations and eigenfunction expansions Math. Nachr. 252 51-69