Absorbing boundary conditions for the Schrödinger equation on finite intervals

Absorbing boundary conditions for Schrödinger equation in a time-dependent interval

“…[10,11] we briefly recall derivation of the approximate ABC for one dimensional Schrödinger equation on a finite interval. Consider the one-dimensional time-dependent Schrödinger equation:…”

“…The square root function can be approximated using the rational function approximation method following [11]:…”

“…One such method, based on the use of dispersion relation was introduced in the Ref. [11] for solving time-dependent Schrödinger equation with ABC on a finite interval. Later, it was improved by Kuska [11] with the use of alternative approximation for dispersion relation.…”

“…Strict mathematical treatment of ABC for different wave equations, including quantum mechanical Schrödinger equation can be found in the Refs. [11][12][13][14][15][16]. For both processes the boundary conditions can be derived by factorization of the differential operator corresponding to a wave equation which in general lead to complicated equations for the boundary conditions The explicit form of such boundary conditions is much more complicated than those of Dirichlet, Neumann and Robin conditions.…”

“…[11] for solving time-dependent Schrödinger equation with ABC on a finite interval. Later, it was improved by Kuska [11] with the use of alternative approximation for dispersion relation. In this paper we extended the results of Kuska to the case of moving boundaries.…”