dorsal/arxiv
View SchemaSpiked and PT-symmetrized decadic potentials supporting elementary N-plets of bound states
| Authors | Miloslav Znojil |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0002083 |
| URL | https://arxiv.org/abs/quant-ph/0002083 |
| DOI | 10.1088/0305-4470/33/38/313 |
| Journal | J. Phys. A: Math. Gen. 33 (2000) 6825 - 6833 |
Abstract
We show that the potential wells with a central spike V(x) = x^{10} + a x^8 + b x^6+ c x^4 + d x^2 + f/x^2 possess arbitrary finite multiplets of elementary exact bound states. The strong asymptotic growth of V(x) implies an ambiguity in the PT-symmetric quantization via complex boundary conditions but the three eligible recipes coincide at our exceptional solutions.
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"abstract": "We show that the potential wells with a central spike\n V(x) = x^{10} + a x^8 + b x^6+ c x^4 + d x^2 + f/x^2 possess arbitrary finite\nmultiplets of elementary exact bound states. The strong asymptotic growth of\nV(x) implies an ambiguity in the PT-symmetric quantization via complex boundary\nconditions but the three eligible recipes coincide at our exceptional\nsolutions.",
"arxiv_id": "quant-ph/0002083",
"authors": [
"Miloslav Znojil"
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"doi": "10.1088/0305-4470/33/38/313",
"journal_ref": "J. Phys. A: Math. Gen. 33 (2000) 6825 - 6833",
"title": "Spiked and PT-symmetrized decadic potentials supporting elementary N-plets of bound states",
"url": "https://arxiv.org/abs/quant-ph/0002083"
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