A fast method to implement non‐local discrete transparent boundary conditions for the Schrödinger equation

Discrete transparent boundary conditions (DTBCs) for the time‐dependent Schrödinger equation were introduced in the numerical simulations of whole space problems in order to reduce the computational domain to a finite region. They include a convolution w.r.t. time with a weakly decaying kernel that leads to very costly numerical evaluation for large‐time simulations. As a remedy we construct approximate DTBCs with a kernel having the form of a finite sum‐of‐exponentials, which can be evaluated in an efficient recursion.