|XXXIX Workshop on Geometric Methods in Physics||28.06-4.07.2020|
|IX School on Geometry and Physics||22-26.06.2020|
One-dimensional Schrödinger operators with complex potentials–singular boundary conditions and exactly solvable Hamiltonians
I will start with a general theory of operators on Hilbert spaces equipped with a conjugation. Then I will discuss closed realizations of Schrödinger operators in one dimension with very general, possibly complex potentials. Next I will discuss exactly solvable Hamiltonians with potentials $1/x^2$ and $1/x$ with complex coupling constants. I will also describe basic properties of the Bessel and Whittaker functions, which are used to solve these problems.
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