Computing wave functions of nonlinear Schroedinger equations: A time-independent approach

Journal Article · Mon Sep 10 04:00:00 EDT 2007 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2007.03.028· OSTI ID:21028257

Chang, S -L ^[1]; Jeng, B -W ^[2]

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1. Center for General Education, Southern Taiwan University of Technology, Tainan 710, Taiwan (China)
2. Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan (China)

We present a novel algorithm for computing the ground-state and excited-state solutions of M-coupled nonlinear Schroedinger equations (MCNLS). First we transform the MCNLS to the stationary state ones by using separation of variables. The energy level of a quantum particle governed by the Schroedinger eigenvalue problem (SEP) is used as an initial guess to computing their counterpart of a nonlinear Schroedinger equation (NLS). We discretize the system via centered difference approximations. A predictor-corrector continuation method is exploited as an iterative method to trace solution curves and surfaces of the MCNLS, where the chemical potentials are treated as continuation parameters. The wave functions can be easily obtained whenever the solution manifolds are numerically traced. The proposed algorithm has the advantage that it is unnecessary to discretize or integrate the partial derivatives of wave functions. Moreover, the wave functions can be computed for any time scale. Numerical results on the ground-state and excited-state solutions are reported, where the physical properties of the system such as isotropic and nonisotropic trapping potentials, mass conservation constraints, and strong and weak repulsive interactions are considered in our numerical experiments.

• OSTI ID: 21028257
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 226; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
APPROXIMATIONS
BOSE-EINSTEIN CONDENSATION
EIGENVALUES
EXCITED STATES
GROUND STATES
ITERATIVE METHODS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PHYSICAL PROPERTIES
POTENTIALS
SCHROEDINGER EQUATION
WAVE FUNCTIONS