| Автор | Carl M Bender |
| Автор | Qinghai Wang |
| Дата выпуска | 2001-04-20 |
| dc.description | It has been conjectured that for ε≥0 the entire spectrum of the non-Hermitian PT-symmetric Hamiltonian H<sub>N</sub> = p<sup>2</sup> + x<sup>2</sup>(ix)<sup>ε</sup>, where N = 2 + ε, is real. Strong evidence for this conjecture for the special case N = 3 was provided in a recent paper by Mezincescu (Mezincescu G A 2000 J. Phys. A: Math. Gen. 33 4911) in which the spectral zeta function Z<sub>3</sub>(1) for the Hamiltonian H<sub>3</sub> = p<sup>2</sup> + ix<sup>3</sup> was calculated exactly. Here, the calculation of Mezincescu is generalized from the special case N = 3 to the region of all N≥2 (ε≥0) and the exact spectral zeta function Z<sub>N</sub>(1) for H<sub>N</sub> is obtained. Using Z<sub>N</sub>(1) it is shown that to extremely high precision (about three parts in 10<sup>18</sup>) the spectrum of H<sub>N</sub> for other values of N such as N = 4 is entirely real. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Comment on a recent paper by Mezincescu |
| Тип | note |
| DOI | 10.1088/0305-4470/34/15/401 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 34 |
| Первая страница | 3325 |
| Последняя страница | 3328 |
| Аффилиация | Carl M Bender; Department of Physics, Washington University, St Louis, MO 63130, USA |
| Аффилиация | Qinghai Wang; Department of Physics, Washington University, St Louis, MO 63130, USA |
| Выпуск | 15 |
