Towards low-scaling algorithms for quantum scattering calculations*

The computational complexity of current algorithms for solving coupled-channel differential equations of quantum scattering theory scales cubically with the number of scattering channels, rendering rigorous calculations on heavy and/or large molecule collisions unfeasible. Here, we report initial steps toward the implementation of a variation-iteration method introduced by Lowell D. Thomas [1], which enables the determination of a single column of the scattering matrix with a more favorable scaling than traditional propagators. 

 

[1] L. D. Thomas, J. Chem. Phys. 70, 2979 (1979).