dorsal/arxiv
View SchemaSome properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant
| Authors | G. Andrei Mezincescu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0002056 |
| URL | https://arxiv.org/abs/quant-ph/0002056 |
| DOI | 10.1088/0305-4470/33/27/308 |
| Journal | J.Phys.A33:4911-4916,2000 |
Abstract
Comparison between the exact value of the spectral zeta function, $Z_{H}(1)=5^{-6/5}[3-2\cos(\pi/5)]\Gamma^2(1/5)/\Gamma(3/5)$, and the results of numeric and WKB calculations supports the conjecture by Bessis that all the eigenvalues of this PT-invariant hamiltonian are real. For one-dimensional Schr\"odinger operators with complex potentials having a monotonic imaginary part, the eigenfunctions (and the imaginary parts of their logarithmic derivatives) have no real zeros.
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"abstract": "Comparison between the exact value of the spectral zeta function,\n$Z_{H}(1)=5^{-6/5}[3-2\\cos(\\pi/5)]\\Gamma^2(1/5)/\\Gamma(3/5)$, and the results\nof numeric and WKB calculations supports the conjecture by Bessis that all the\neigenvalues of this PT-invariant hamiltonian are real. For one-dimensional\nSchr\\\"odinger operators with complex potentials having a monotonic imaginary\npart, the eigenfunctions (and the imaginary parts of their logarithmic\nderivatives) have no real zeros.",
"arxiv_id": "quant-ph/0002056",
"authors": [
"G. Andrei Mezincescu"
],
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"quant-ph",
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"math.MP"
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"doi": "10.1088/0305-4470/33/27/308",
"journal_ref": "J.Phys.A33:4911-4916,2000",
"title": "Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant",
"url": "https://arxiv.org/abs/quant-ph/0002056"
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