Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
We consider the difference Schrödinger equation ψ (z+h)+ ψ (z-h)+v(z)ψ (z) = 0, where z is a complex variable, h > 0 is a parameter, and v is an analytic function. As h → 0, analytic solutions to this equation have a simple WKB behavior near the points where v(z) ≠ ± 2. We study analytic solutions near the points z0 satisfying v(z0) = ± 2 and v′ (z0) ≠ 0. These points play the same role as simple turning points for the differential equation ψ″ (z) + v(z)ψ (z) = 0. In an h-independent complex neighborhood of such a point, we derive uniform asymptotic expansions for analytic solutions to the difference equation.
Язык оригинала | английский |
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Страницы (с-по) | 4413-4447 |
Число страниц | 35 |
Журнал | SIAM Journal on Mathematical Analysis |
Том | 51 |
Номер выпуска | 6 |
DOI | |
Состояние | Опубликовано - 1 янв 2019 |
ID: 48480873