Point interactions: PT-hermiticity and reality of the spectrum

Letters in Mathematical Physics

Volumn 59, Issue 3, 2002, Pages 227-242

  Albeverio, Sergio ^a,b   Fei, Shao Ming ^a,c   Kurasov, Pavel ^d  

^a UNIVERSITY OF BONN   (Germany)

^b SFB 256 Bonn BiBoS ^*  (Germany)

^c CAPITAL NORMAL UNIVERSITY   (China)

^d LUND INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Point interactions; PT symmetric quantum mechanics

Indexed keywords

EID: 0012878839     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1015559117837     Document Type: Article

References (34)

1. Albeverio, S., Da̧browski, L. and Kurasov, P.: Symmetries of Schrödinger operators with point interactions, Lett. Math. Phys. 45 (1998), 33-47.
2. Albeverio, S., Fei, S. M. and Kurasov, P.: Gauge fields, point interactions and few-body problems in one dimension, SFB256 - Preprint No. 614, Rheinische Friedrich-Wilhelms-Universität-Bonn, September 1999.
3. Albeverio, S., Fei, S. M. and Kurasov, P.: N-Body Problems with 'Spin'-Related Contact Interactions in One Dimensional, Rep. Math. Phys. 47 (2001), 157-165.
4. Albeverio, S., Gesztesy, F., Høegh-Krohn, R. and Holden, H.: Solvable Models in Quantum Mechanics, Springer, New York, 1988.
5. Albeverio, S. and Kurasov, P.: Singular perturbations of differential operators. In: Solvable Schrödinger type operators, London Math. Soc. Lecture Note Ser. 271, Cambridge Univ. Press, Cambridge, 2000.
6. Bender, C. M. and Boettcher, S. Real spectra in non-Hermitian Hamiltonians having PT symmetry, Phys. Rev. Lett. 80 (1998), 5243-5246.
7. Bender, C. M., Boettcher, S., Jones, H. F. and Savage, V. M.: Complex square well - a new exactly solvable quantum mechanical model, J. Phys. A 32 (1999), 6771-6781.
8. Bender, C. M., Boettcher, S. and Meisinger, P. N.: PT-symmetric quantum mechanics, J. Math. Phys. 40 (1999), 2201-2229.
9. Bender, C. M., Cooper, F., Meisinger, P. N. and Savage, V. M.: Variational ansatz for PT-symmetric quantum mechanics, Phys. Lett. A 259 (1999), 224-231.
10. Bender, C. M. and Dunne, G. V.: Large-order perturbation theory for a non-Hermitian PT-symmetric Hamiltonian, J. Math. Phys. 40 (1999), 4616-4621.
11. Bender, C. M., Dunne, G. V. and Meisinger, P. N.: Complex periodic potentials with real band spectra, Phys. Lett. A 252 (1999), 272-276.
12. Boman, J. and Kurasov, P.: Finite rank singular perturbations and distributions with discontinuous test functions, Proc. Amer. Math. Soc. 126 (1998), 1673-1683.
13. Coutinho, F. A. B., Nogami, Y. and Lauro Tomio: Time-reversal aspect of the point interactions in one-dimensional quantum mechanics, J. Phys. A 32 (1999), L133-L136.
14. Demkov, Yu. N. and Ostrovsky, V. N.: Zero-range potentials and their applications in atomic physics, Plenum, New York, 1988.
15. Dorey, P., Dunning, C. and Tateo, R.: Supersymmetry and the spontaneous breakdown of PT-symmetry, J. Phys. A 34 (2001), L391-L400.
16. Dorey, P., Dunning, C. and Tateo, R.: Spectral equivalence, bethe ansatz, and reality properties in PT-symmetric quantum mechanics, J. Phys. A 34 (2001), 5679-5704.
17. 3 non-Hermitian potential, J. Phys. A 34 (2001), L271-L277.
18. 2 + iαX Hamiltonian, J. Phys. A 34 (2001), 5593-5602.
19. Kurasov, P.: Distribution theory for discontinuous test functions and differential operators with generalized coefficients, J. Math. Anal. Appl. 201 (1996), 297-323.
20. Kurasov, P.: Energy dependent boundary conditions and the few-body scattering problem, Rev. Math. Phys. 9 (1997), 853-906.
21. Lévai, G. and Znojil, M.: Systematic search for PT-symmetric potentials with real energy spectra, J. Phys. A 33 (2000), 7165-7180.
22. Naboko, S. N.: Functional model of perturbation theory and its applications to scattering theory (Russian) In: Boundary Value Problems of Math. Phys. 10. Trudy Mat. Inst. Steklov. 147 (1980), 86-114.
23. Naboko, S. N.: Conditions for the existence of wave operators in the nonselfadjoint case (Russian) In: Wave Propagation, Scattering Theory (Russian), Probl. Mat. Fiz. 12, Leningrad. Univ., Leningrad, 1987, pp. 132-155.
24. Pavlov, B.: On a non-selfadjoint Schrödinger operator (in Russian), Prob. Math. Phys. I (1966), 102-132.
25. Pavlov, B. S.: Dilation theory and spectral analysis of nonselfadjoint differential operators (Russian), In: Mathematical Programming and Related Questions, (Proc. Seventh Winter School, Drogobych, 1974), Theory of Operators in Linear Spaces (Russian), Central. Ekonom. Mat. Inst. Akad. Nauk SSSR, Moscow, 1976, pp. 3-69.
26. Šeba, P.: The generalized point interaction in one dimension, Czech. J. Phys. B 36 (1986), 667-673.
27. Znojil, M.: Non-Hermitian matrix description of the PT-symmetric anharmonic oscillators, J. Phys. A 32 (1999), 7419-7428.
28. Znojil, M.: Exact solution for Morse oscillator in PT-symmetric quantum mechanics, Phys. Lett. A 264 (1999), 108-111.
29. Znojil, M.: PT-symmetric harmonic oscillators, Phys. Lett. A 259 (1999), 220-223.
30. Znojil, M.: Spiked and PT-symmetrized decadic potentials supporting elementary N-plets of bound states, J. Phys. A 33 (2000), 6825-6833.
31. Znojil, M.: PT-symmetrically regularized Eckart, Pöschl-Teller and Hulthén potentials, J. Phys. A 33 (2000), 4561-4572.
32. Znojil, M., Cannata, F., Bagchi, B. and Roychoudhury, R. Supersymmetry without Hermiticity within PT symmetric quantum mechanics, Phys. Lett. B 483 (2000), 284-289.
33. Znojil, M. and Lévai, G.: The Coulomb-harmonic oscillator correspondence in PT symmetric quantum mechanics, Phys. Lett. A 271 (2000), 327-333.
34. Znojil, M. and Tater, M.: Complex Calogero model with real energies, J. Phys. A 34 (2001), 1793-1803.