We discuss realizations of \(L:=-\partial _x^2+V(x)\) as closed operators on \(L^2]a,b[\), where V is complex, locally integrable and may have an arbitrary behavior at (finite or infinite) endpoints a and b. The main tool of our analysis is Green’s operators, that is, various right inverses of L.

中文翻译：

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具有复数势的一维Schrödinger算子

我们将\（L：=-\ partial _x ^ 2 + V（x）\）的实现作为\（L ^ 2] a，b [\）上的封闭算符进行讨论，其中V是复杂的，局部可积分的并且可能具有在（有限或无限）端点a和b处的任意行为。我们分析的主要工具是Green的运算符，即L的各个右逆。