The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
Spectral equivalences, Bethe ansatz equations, and reality properties in 𝒫𝒯-symmetric quantum mechanics
Open accessAbstract
The one-dimensional Schrödinger equation for the potential x 6 + α x 2 + l ( l + 1)/ x 2 has many interesting properties. For certain values of the parameters l and α the equation is in turn supersymmetric (Witten) and quasi-exactly solvable (Turbiner), and it also appears in Lipatov's approach to high-energy QCD. In this paper we signal some further curious features of these theories, namely novel spectral equivalences with particular second- and third-order differential equations. These relationships are obtained via a recently observed connection between the theories of ordinary differential equations and integrable models. Generalized supersymmetry transformations acting at the quasi-exactly solvable points are also pointed out, and an efficient numerical procedure for the study of these and related problems is described. Finally we generalize slightly and then prove a conjecture due to Bessis, Zinn-Justin, Bender and Boettcher, concerning the reality of the spectra of certain -symmetric quantum mechanical systems.
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Citations
Cites
(1998) · doi:10.1103/physrevlett.80.5243 · Cited by 6,280
Quantum Field Theory and Critical Phenomena
Zinn-Justin, J. (2002) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198509233.001.0001 · Cited by 5,116
Dynamical breaking of supersymmetry
Witten, E. (1981) · Nuclear Physics B · doi:10.1016/0550-3213(81)90006-7 · Cited by 3,775
𝓟𝓣-symmetric quantum mechanics
Bender, C. M., Boettcher, S., & Meisinger, P. N. (1999) · Journal of Mathematical Physics · doi:10.1063/1.532860 · Cited by 1,373
On the Connection Formulas and the Solutions of the Wave Equation
Langer, R. E. (1937) · Physical Review · doi:10.1103/physrev.51.669 · Cited by 1,011
Quasi-exactly-solvable problems andsl(2) algebra
Turbiner, A. V. (1988) · Communications in Mathematical Physics · doi:10.1007/bf01466727 · Cited by 723
Quasi-exactly solvable models in quantum mechanics
Ushveridze, A. G. (2017) · CRC Press eBooks · doi:10.1201/9780203741450 · Cited by 498
Supersymmetry and the spontaneous breakdown of 𝒫𝒯 symmetry
Dorey, P., Dunning, C., & Tateo, R. (2001) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/34/28/102 · Cited by 278
Self-citationSOLVING THE SCHRÖDINGER EQUATION FOR BOUND STATES WITH MATHEMATICA 3.0
Wolfgang Lucha, B., & Schöberl, F. F. (1999) · International Journal of Modern Physics C · doi:10.1142/s0129183199000450 · Cited by 275
Equivalence of unstable anharmonic oscillators and double wells
Buslaev, V, & Grecchi, V (1993) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/26/20/035 · Cited by 217
Cited by
Making sense of non-Hermitian Hamiltonians
Bender, C. M. (2007) · Reports on Progress in Physics · doi:10.1088/0034-4885/70/6/r03 · Cited by 2,984
Introduction to 𝒫𝒯-symmetric quantum theory
Bender, C. M. (2005) · Contemporary Physics · doi:10.1080/00107500072632 · Cited by 489
Faster than Hermitian quantum mechanics
Bender, C. M., Brody, D. C., Jones, H. F., & Meister, B. K. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.040403 · Cited by 417
Supersymmetry and the spontaneous breakdown of 𝒫𝒯 symmetry
Dorey, P., Dunning, C., & Tateo, R. (2001) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/34/28/102 · Cited by 278
Self-citationObservation of PT-symmetric quantum interference
Klauck, F., Teuber, L., Ornigotti, M., Heinrich, M., Scheel, S., & Szameit, A. (2019) · Nature Photonics · doi:10.1038/s41566-019-0517-0 · Cited by 168
Metadata
- Authors
- Dorey, P., Dunning, C., & Tateo, R.
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 2001-07-06
- Volume
- 34
- Issue
- 28
- Pages
- 5679-5704
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2040246371
- Cited by
- 543
- References
- 18
- FWCI
- 20.27
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Dorey, P., Dunning, C., & Tateo, R. (2001). Spectral equivalences, Bethe ansatz equations, and reality properties in 𝒫𝒯-symmetric quantum mechanics. Journal of Physics A: Mathematical and General. https://doi.org/10.1088/0305-4470/34/28/305
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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