Part 2: Implementation. Multiresolution of the one dimensional free-particle propagator.

A novel method to integrate the time-dependent Schrödinger equation within the framework of multiresolution analysis is presented.

Evgueni Dinvay with glasses.

Evgueni Dinvay. Photo: Cathrine Strøm, UiO. 

By Evgueni Dinvay
Published Dec. 8, 2024

The method is based on symplectic splitting algorithms to separate the kinetic and potential parts of the corresponding propagator. The semigroup associated with the free-particle Schrödinger operator is represented in a multiwavelet basis. The propagator is effectively discretized with a contour deformation technique, which overcomes the challenges presented by previous discretization methods. The discretized operator is then employed in simple numerical simulations to test the validity of the implementation and to benchmark its precision.

Publication: 2024.12.08, https://www.sciencedirect.com/science/article/pii/S0010465524003618#gsp0030 

Tags: Hylleraas Centre, time-dependent Schrödinger equation, splitting algorithms, free-particle Schrödinger operator i
Published Dec. 8, 2024 1:05 PM - Last modified Dec. 19, 2024 1:06 PM