Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant
Mezincescu, G. Andrei
arXiv, 0002056 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-02-21
Classification:  Quantum Physics,  Condensed Matter,  High Energy Physics - Theory,  Mathematical Physics 
@article{0002056,
     author = {Mezincescu, G. Andrei},
     title = {Some properties of eigenvalues and eigenfunctions of the cubic
  oscillator with imaginary coupling constant},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0002056}
}

Mezincescu, G. Andrei. Some properties of eigenvalues and eigenfunctions of the cubic
  oscillator with imaginary coupling constant. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0002056/