Symplectic algorithm for use in computing the time-independent Schrodinger equation

We present an improved symplectic scheme-shooting method (ISSSM) for solving the one-dimensional time-independent Schrodinger equation. This method is applied to computations of the eigenvalues and wave functions of the hydrogen molecule (H-2) and a Morse potential; the method is also applied to computations of the parameters and wave functions of a soft potential. The numerical results are in good agreement with the exact ones or other numerical ones and illustrate that the ISSSM is more effective than the SSSM. Then the ISSSM is extended to solutions of the two-dimensional time-independent Schrodinger equation. The eigenvalues of the two-dimensional harmonic oscillator and the two-dimensional Henon-Heiles potential are calculated by using the ISSSM. The numerical results illustrate that our method is stable and convergent for two dimensions. (C) 2002 John Wiley Sons, Inc.