A Chebychev propagator for inhomogeneous Schr\"odinger equations
Mamadou Ndong, Hillel Tal-Ezer, Ronnie Kosloff, Christiane P. Koch
TL;DR
This paper introduces a Chebychev polynomial-based propagation scheme for solving inhomogeneous Schr"odinger equations, improving computational efficiency and accuracy in applications like optimal control and reactive scattering.
Contribution
It develops a novel Chebychev polynomial expansion method for inhomogeneous Schr"odinger equations, with multiple variants and demonstrated effectiveness in practical examples.
Findings
Enhanced convergence behavior
Improved numerical efficiency
Effective in optimal control applications
Abstract
We present a propagation scheme for time-dependent inhomogeneous Schr\"odinger equations which occur for example in optimal control theory or in reactive scattering calculations. A formal solution based on a polynomial expansion of the inhomogeneous term is derived. It is subjected to an approximation in terms of Chebychev polynomials. Different variants for the inhomogeneous propagator are demonstrated and applied to two examples from optimal control theory. Convergence behavior and numerical efficiency are analyzed.
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