| Автор | M V Berry |
| Дата выпуска | 1982-12-01 |
| dc.description | The coefficient r for reflection above a barrier V(x) is computed semiclassically (i.e. as h(cross) to 0) employing an exact multiple-reflection series whose mth term is a (2m+1)-fold integral. If V(x) is analytic, all terms have the same semiclassical order (exp(-h(cross)<sup>-1</sup>)); the multiple integrals are evaluated exactly and the series summed. If V(x) has a discontinuous Nth derivative, the term m=1 dominates semiclassically and gives r approximately h(cross)<sup>N</sup>. If V(x) has all derivatives continuous but possesses an essential singularity on the real axis, the term m=1 again dominates semiclassically, and for V approximately exp(- mod x mod <sup>-n</sup>) gives r approximately exp(-h(cross)<sup>-n</sup>(n+1)/) with an oscillatory factor corresponding to transmission resonances. The formulae are illustrated by computations of mod r mod <sup>2</sup> for four potentials with different continuity properties and show the limiting asymptotics emerging only when the de Broglie wavelength is less than 1% of the barrier width and mod r mod <sup>2</sup> approximately 10<sup>-1000</sup>. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Semiclassically weak reflections above analytic and non-analytic potential barriers |
| Тип | paper |
| DOI | 10.1088/0305-4470/15/12/021 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 15 |
| Первая страница | 3693 |
| Последняя страница | 3704 |
| Аффилиация | M V Berry; H.H. Wills Phys. Lab., Bristol, UK |
| Выпуск | 12 |
