Paper Info
Title
Efficient numerical methods for the time-dependent schroedinger equation for molecules in intense laser fields
Abstract
We present an accurate method for the nonperturbative numerical solution of the Time-Dependent Schroedinger Equation, TDSE, for molecules in intense laser fields, using cylindrical/polar coordinates systems. For cylindrical coordinates systems, after use of a split-operator method which separates the z direction propagation and the (x,y) plane propagation, we approximate the wave function in each (x,y) section by a Fourier series ($\sum c_m(\rho)e^{im\phi}$) which offers an exponential convergence in the φ direction and is naturally applicable for polar coordinates systems. The coefficients (cm(ρ)) are then calculated by a Finite Difference Method (FDM) in the ρ direction. We adopt the Crank-Nicholson method for the temporal propagation. The final linear system consists of a set of independent one-dimensional (ρ) linear systems and the matrix for every one-dimensional linear systems is sparse, so the whole linear system may be very efficiently solved. We note that the Laplacean operator in polar/cylindrical coordinate has a singular term near the origin. We present a method to improve the numerical stability of the Cranck-Nicholson method in this case. We illustrate the improved stability by calculating several eigenstates of $H_3^{++}$ with propagation in imaginary time. Two methods of spatial discretization are also compared in calculations of Molecular High Order Harmonic Generation, MHOHG.
Year
DOI
Venue
2009
10.1007/978-3-642-12659-8_8
HPCS
Keywords
Field
DocType
efficient numerical method,temporal propagation,cranck-nicholson method,final linear system,crank-nicholson method,one-dimensional linear system,plane propagation,linear system,accurate method,direction propagation,intense laser field,time-dependent schroedinger equation,split-operator method,polar coordinate,numerical method,fourier series,numerical stability,finite difference method,coordinate system
Cylindrical coordinate system,Mathematical optimization,Linear system,Computer science,Mathematical analysis,Parallel computing,Schrödinger equation,Polar coordinate system,Finite difference method,Numerical analysis,Numerical stability,Eigenvalues and eigenvectors
Conference
Volume
ISSN
ISBN
5976
0302-9743
3-642-12658-8
Citations 
PageRank 
References 
0
0.34
1
Authors
2
Name
Order
Citations
PageRank
André D. Bandrauk1439.52
H. Z. Lu201.01