dorsal/arxiv
View SchemaNon-Hermitian matrix description of the PT symmetric anharmonic oscillators
| Authors | Miloslav Znojil |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9906029 |
| URL | https://arxiv.org/abs/quant-ph/9906029 |
| DOI | 10.1088/0305-4470/32/42/313 |
| Journal | J.Phys.A32:7419-7428,1999 |
Abstract
Schroedinger equation H \psi=E \psi with PT - symmetric differential operator H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at a>0. The proof of this non-variational construction is given. Our Taylor series form of \psi complements and completes the recent terminating solutions as obtained for certain couplings \delta at the less common negative a.
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"abstract": "Schroedinger equation H \\psi=E \\psi with PT - symmetric differential operator\nH=H(x) = p^2 + a x^4 + i \\beta x^3 +c x^2+i \\delta x = H^*(-x) on\nL_2(-\\infty,\\infty) is re-arranged as a linear algebraic diagonalization at\na\u003e0. The proof of this non-variational construction is given. Our Taylor series\nform of \\psi complements and completes the recent terminating solutions as\nobtained for certain couplings \\delta at the less common negative a.",
"arxiv_id": "quant-ph/9906029",
"authors": [
"Miloslav Znojil"
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"quant-ph"
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"doi": "10.1088/0305-4470/32/42/313",
"journal_ref": "J.Phys.A32:7419-7428,1999",
"title": "Non-Hermitian matrix description of the PT symmetric anharmonic oscillators",
"url": "https://arxiv.org/abs/quant-ph/9906029"
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