Numerical techniques for the solution of the time-dependent Schroedinger equation and their parallel implementation

Thesis/Dissertation · Mon Jan 01 04:00:00 EST 1990

OSTI ID:7158685

Saied, F

The author investigates numerical techniques for the solution of the time-dependent Schroedinger equation in one and two space dimensions. A framework is introduced for constructing finite-difference schemes based on Pade approximations for both the time and space discretization, and this framework is applied to construct high-order finite-difference schemes for Schroedinger's equation in conjunction with an operator splitting approach. Three level schemes as an alternative to operator splitting are also discussed. The accuracy and stability of these methods are studied, and their efficiencies are compared. Results of some numerical comparisons of the methods are presented. For two space dimensions, some of the new techniques proposed include a split-step Crank-Nicolson scheme, where the implicit equations at each time step can be solved by a fast Poisson solver. The two-dimensional methods have ADI (alternating direction implicit) analogues which reduce the complexity of the computations.

• Research Organization: Yale Univ., New Haven, CT (United States)
• OSTI ID: 7158685
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ACCURACY
COMPUTERS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
HYPERCUBE COMPUTERS
ITERATIVE METHODS
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS
PROGRAMMING
SCHROEDINGER EQUATION
TWO-DIMENSIONAL CALCULATIONS
WAVE EQUATIONS