We study the behavior of eigenfunctions of the Schrödinger operator with potential having power, exponential or super-exponential growth at infinity and discontinuities on manifolds in . We use a connection between the domain of analyticity of the main symbol of the parametrix at infinity or near singularities of and the behavior of eigenfunctions at infinity or near singularities of potentials. Our approach is based on a general calculus of pseudodifferential operators with analytic symbols.
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Vladimir S. Rabinovich, Pseudodifferential Operators with Analytic Symbols and Estimates for Eigenfunctions of Schrödinger Operators. Z. Anal. Anwend. 21 (2002), no. 2, pp. 351–370DOI 10.4171/ZAA/1082