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Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials
Colloquium| Speaker: | Joel Smoller, University of Michigan |
| Location: | 1147 MSB |
| Start time: | Mon, May 18 2009, 4:10PM |
A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati equation. We explain the general strategy for applying these estimates and illustrate the method in typical examples, where the approximate solutions are obtained by glueing together WKB and Airy solutions of the corresponding one-dimensional Schrödinger equations. (This is joint work with Felix Finster.)