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Systematic search for 𝒫𝒯-symmetric potentials with real energy spectra
Open accessAbstract
Changes of coordinates represent one of the most effective ways of deriving solvable potentials from ordinary differential equations for separate special functions. Here we relax the standard Hermiticity requirement and find an innovative construction which leads to unusual, complex potentials. Their energy spectrum is shown to stay real after a weakening of the Hermiticity of the Schrödinger equation to its mere invariance under the combined (parity) and (time-reversal) symmetry. This ultimately results in richer bound-state spectra. Some of our new exactly solvable potentials generalize the current textbook models. Details are given for constructions based on the hypergeometric and confluent hypergeometric special functions.
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Cited by
Parity–time synthetic photonic lattices
Regensburger, A., Bersch, C., Miri, M.-A., Onishchukov, G., Christodoulides, D. N., & Peschel, U. (2012) · Nature · doi:10.1038/nature11298 · Cited by 2,019
PT-symmetry in honeycomb photonic lattices
Szameit, A., Rechtsman, M. C., Bahat-Treidel, O., & Segev, M. (2011) · Physical Review A · doi:10.1103/physreva.84.021806 · Cited by 280
Metadata
- Authors
- Lévai, G., & Znojil, M.
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 2000-09-29
- Volume
- 33
- Issue
- 40
- Pages
- 7165-7180
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2255317856
- Cited by
- 274
- References
- 0
- FWCI
- 12.33
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Lévai, G., & Znojil, M. (2000). Systematic search for 𝒫𝒯-symmetric potentials with real energy spectra. Journal of Physics A: Mathematical and General. https://doi.org/10.1088/0305-4470/33/40/313
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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