Adaptive Time Propagation for Time-dependent Schrödinger equations

Schrödinger equations with time - dependent

We present some general results for the time-dependent mass Hamiltonian problem with H = − 2e∂xx + h(2)(t)e2νx2. This Hamiltonian corresponds to a time-dependent mass (TM) Schrödinger equation with the restriction that there are only P 2 and X2 terms. We give the specific transformations to a different quantum Schrödinger(TQ) equation and to a different time-dependent oscillator (TO) equation. ...

A Local Strong form Meshless Method for Solving 2D time-Dependent Schrödinger Equations

This paper deals with the numerical solutions of the 2D time dependent Schr¨odinger equations by using a local strong form meshless method. The time variable is discretized by a finite difference scheme. Then, in the resultant elliptic type PDEs, special variable is discretized with a local radial basis function (RBF) methods for which the PDE operator is also imposed in the local matrices. Des...

Time - dependent mass Schrödinger equations . III . Example

We attack the specific time-dependent Hamiltonian problem H = − 2 ( to t a ∂xx+ 1 2ω 2 ( t to )b x2. This corresponds to a time-dependent mass (TM) Schrödinger equation. We give the specific transformations to a different time-dependent quadratic Schrödinger equations (TQ) and to a different time-dependent oscillator (TO) equation. For each Schrödinger system, we give the Lie algebra of space-t...

On Magnus Integrators for Time-Dependent Schrödinger Equations

Global error control of the time-propagation for the Schrödinger equation with a time-dependent Hamiltonian

We use a posteriori error estimation theory to derive a relation between local and global error in the propagation for the time-dependent Schrödinger equation. Based on this result, we design a class of h,padaptive Magnus–Lanczos propagators capable of controlling the global error of the time-stepping scheme by only solving the equation once. We provide results for models of several different s...