title: Accurate complex scaling of three dimensional numerical potentials.
abstract: The complex scaling method, which consists in continuing spatial coordinates into the complex plane, is a well-established method that allows to compute resonant eigenfunctions of the time-independent Schrödinger operator. Whenever it is desirable to apply the complex scaling to investigate resonances in physical systems defined on numerical discrete grids, the most direct approach relies on the application of a similarity transformation to the original, unscaled Hamiltonian. We show that such an approach can be conveniently implemented in the Daubechies wavelet basis set, featuring a very promising level of generality, high accuracy, and no need for artificial convergence parameters. Complex scaling of three dimensional numerical potentials can be efficiently and accurately performed. By carrying out an illustrative resonant state computation in the case of a one-dimensional model potential, we then show that our wavelet-based approach may disclose new exciting opportunities in the field of computational non-Hermitian quantum mechanics.
authors.affiliation: European Synchrotron Radiation Facility, 6 rue Horowitz, BP220 38043 Grenoble Cedex 9, France. alessandro.cerioni@esrf.fr
authors.forename: Alessandro
authors.initials: A
authors.lastname: Cerioni
authors.forename: Luigi
authors.initials: L
authors.lastname: Genovese
authors.forename: Ivan
authors.initials: I
authors.lastname: Duchemin
authors.forename: Thierry
authors.initials: T
authors.lastname: Deutsch