Low-complexity approximations with least-squares formulation of the time-dependent Schrödinger equation

2025/09/16 by Dupuy, Mi-Song, Ehrlacher, Virginie, Guillot, Clément
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.13005

Abstract

We propose new methods designed to numerically approximate the solution to the time dependent Schrödinger equation, based on two types of ansatz: tensors, and approximation by a linear combination of gaussian wave packets. In both cases, the method can be seen as a restricted optimization problem, which can be solved by adapting either the Alternating Least Square algorithm in the tensor case, or some greedy algorithm in the gaussian wavepacket case. We also discuss the efficiency of both approaches.

Citations

• Time-integration of Gaussian variational approximation for the magnetic Schrödinger equation
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