New, Highly Accurate Propagator for the Linear and Nonlinear Schrödinger Equation

Details New, Highly Accurate Propagator for the Linear and Nonlinear Schrödinger Equation New, Highly Accurate Propagator for the Linear and Nonlinear Schrödinger Equation

2012-04-17

arxiv.org/abs/1204.3766v1

Journal of Scientific Computing (2012)

Physics

Quantum Physics

14 pages

Scientific paper

10.1007/s10915-012-9583-x

A propagation method for the time dependent Schr\"odinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form u_t -Gu = s where G is a operator (matrix) and u is a time-dependent solution vector. Highly accurate methods, based on polynomial approximation of a modified exponential evolution operator, had been developed already for this type of problems where G is a linear, time independent matrix and s is a constant vector. In this paper we will describe a new algorithm for the more general case where s is a time-dependent r.h.s vector. An iterative version of the new algorithm can be applied to the general case where G depends on t or u. Numerical results for Schr\"odinger equation with time-dependent potential and to non-linear Schr\"odinger equation will be presented.

Affiliated with

Also associated with

No associations

Rating

New, Highly Accurate Propagator for the Linear and Nonlinear Schrödinger Equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with New, Highly Accurate Propagator for the Linear and Nonlinear Schrödinger Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New, Highly Accurate Propagator for the Linear and Nonlinear Schrödinger Equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-289787