DOI

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 оригиналаанглийский
Страницы (с-по)4413-4447
Число страниц35
ЖурналSIAM Journal on Mathematical Analysis
Том51
Номер выпуска6
DOI
СостояниеОпубликовано - 1 янв 2019

    Предметные области Scopus

  • Анализ
  • Вычислительная математика
  • Прикладная математика

ID: 48480873