A Note on $p$-Adic Schrödinger Equations with Nonlocal Potentials
Анотація
Ми розглядаємо $p$-адичне рівняння Шредінгера $i\partial_tu=(\mathbf{D}^\alpha+\mathbf V(t))u$ із залежним від часу нелокальним потенціалом $\mathbf V$, визначеним на полі $p$-адичних чисел $\mathbb{Q}_p$. Ми будуємо розв'язок $u$ у просторі $\mathcal H=L^2(\mathbb{Q}_p)$, апроксимуючи його послідовністю функцій, які задовольняють аналогічні рівняння у скінченновимірних підпросторах $E_N\subset\mathcal H$.
Mathematical Subject Classification 2020: 34L15, 34L20, 35R10
Ключові слова:
оператор Владимирова, нелокальний потенціал, рівняння Шредінгера, скінченновимірні апроксимаціїПосилання
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