Papers › Semi-classical Schrödinger numerics in the residual representation
Semi-classical Schrödinger numerics in the residual representation
Christoph Nölle
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed representation of quantum mechanics as a residual theory on top of classical Hamiltonian mechanics transforms a semi-classical wave function into a slowly-fluctuating, spatially confined residual wave function. This representation is therefore well-suited for the numerical solution of semi-classical quantum problems. In this note I outline the formulation of the theory and demonstrate its applicability to a set of semi-classical scenarios, including a discussion of limitations. I work out the connection to established numerical approaches, such as the Gaussian beam approximation and the Gaussian wave packet transform by Russo and Smereka. A prototypical implementation of the method has been published as open-source software.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections