| Автор | Miloslav Znojil |
| Дата выпуска | 1999-06-18 |
| dc.description | In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere T invariance the superposition V(x) = x<sup>2</sup>+Ze<sup>2</sup>/x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze<sup>2</sup> = if) and regularized by a purely imaginary shift of x. This model is quasi-exactly solvable: We show that at each excited, (N + 1)th harmonic-oscillator energy E = 2N+3 there exists not only the well known harmonic oscillator bound state (at the vanishing charge f = 0) but also a normalizable (N + 1)-plet of the further elementary Sturmian eigenstates <sub>{n}</sub>(x) at eigencharges f = f<sub>{n}</sub><0, n = 0,1, ... ,N. Beyond the smallest multiplicities N we recommend perturbative methods for their construction. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable |
| Тип | paper |
| DOI | 10.1088/0305-4470/32/24/318 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 32 |
| Первая страница | 4563 |
| Последняя страница | 4570 |
| Аффилиация | Miloslav Znojil; Ústav jadernéfyziky AV CR, 250 68 Rez, Czech Republic |
| Выпуск | 24 |
