Complex WKB analysis of energy-level degeneracies of non-Hermitian Hamiltonians

Journal of Physics A: Mathematical and General

Volumn 34, Issue 6, 2001, Pages

  Bender, Carl M ^a   Berry, Michael ^b   Meisinger, Peter N ^a   Savage, Van M ^a   Simsek, Mehmet ^a,c  

^a WASHINGTON UNIVERSITY   (United States)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

^c GAZI UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035895850     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/6/101     Document Type: Article

References (15)

1. Delabaere E and Pham F 1998 Eigenvalues of complex Hamiltonians with PT symmetry. II Phys. Lett. A 250 29-32
2. Delabaere E and Trinh D T 2000 Spectral analysis of the cubic oscillator J. Phys. A: Math. Gen. 33 8771-96
3. Methods of complex WKB theory are discussed in: Berry M V and Mount K E 1972 Semiclassical approximations in wave mechanics Rep. Prog. Phys. 35 315-97
4. Dingle R B 1973 Asymptotic Expansions: Their Derivation and Interpretation (New York: Academic)
5. Voros A 1983 The return of the quartic oscillator. The complex WKB method Ann. Inst. H Poincaré, Phys. Theor. 39 211-338
6. Delabaere E, Dillinger H and Pham F 1997 Exact semiclassical expansions for one-dimensional quantum oscillators J. Math. Phys. 38 6126-84 and references therein
7. Bender C M and Boettcher S 1998 Real spectra in non-Hermitian Hamiltonians having PT symmetry Phys. Rev. Lett. 80 5243-6
8. Bender C M, Boettcher S and Meisinger P N 1999 PT-symmetric quantum mechanics J. Math. Phys. 40 2201-29 and references therein
9. Bender C M and Orszag S A 1978 Advanced Mathematical Methods for Scientists and Engineers (New York: McGraw-Hill) ch 10
10. Mezincescu G A 2000 Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant J. Phys. A: Math. Gen. 33 4911-6 and references therein
11. Bender C M and Wang Q 2001 Comment on a paper by Mezincescu J. Phys. A: Math. Gen. at press
12. Shin K C 2000 On the eigenproblems of PT-symmetric oscillators Preprint math-ph/0007006
13. Delabaere E and Pham F 1998 Eigenvalues of complex Hamiltonians with PT symmetry. I Phys. Lett. A 250 25-8
14. Simon B 1970 Coupling-constant analyticity for the anharmonic oscillator Ann. Phys., NY 58 76-136
15. Bender C M and Orszag S A 1978 Advanced Mathematical Methods for Scientists and Engineers (New York: McGraw-Hill) ch 7