| Автор | Piotr Milczarski |
| Автор | Stefan Giller |
| Дата выпуска | 2000-01-21 |
| dc.description | A mechanism for the JWKB formulae in one-dimensional quantum mechanics to quantize energy levels exactly is discussed. This mechanism is most easily applied when considered potentials are represented (by a suitable change of variable) as periodic ones. To be successful, the mechanism demands potentials with no more than one second-order pole and no more than two (occasionally four) turning points in the basic period strips. It then selects 11 potentials which have been known in the literature for a long time. It is also shown that the exactness of the supersymmetric (SUSY) JWKB formulae for these 11 potentials follows directly from the corresponding exactness of the conventional ones being a consequence of the singularity structures of the potentials. A relation of these singularity structures to the shape invariance symmetry of the quantized potentials is shown to guarantee the conventional and SUSY JWKB formulae to be exact simultaneously. The relevant two non-perturbative theorems describing these facts are formulated and proved. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Exactness of conventional and supersymmetric JWKB formulae and their relation to the shape invariance property of potentials |
| Тип | paper |
| DOI | 10.1088/0305-4470/33/2/311 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 33 |
| Первая страница | 357 |
| Последняя страница | 393 |
| Аффилиация | Piotr Milczarski; Theoretical Physics Department II, University of Lódz, Pomorska 149/153, 90-236 Lódz, Poland |
| Аффилиация | Stefan Giller; Theoretical Physics Department II, University of Lódz, Pomorska 149/153, 90-236 Lódz, Poland |
| Выпуск | 2 |
