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Solution of time-independent Schrödinger equation by the imaginary time propagation method. (English) Zbl 1110.65096

Summary: Numerical solution of eigenvalues and eigenvectors of large matrices originating from discretization of linear and nonlinear Schrödinger equations using the imaginary time propagation (ITP) method is described. Convergence properties and accuracy of 2nd and 4th order operator-splitting methods for the ITP method are studied using numerical examples. The natural convergence of the method is further accelerated with a new dynamic time step adjustment method. The results show that the ITP method has better scaling with respect to matrix size as compared to the implicitly restarted Lanczos method. An efficient parallel implementation of the ITP method for shared memory computers is also demonstrated.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
65Y05 Parallel numerical computation
65F15 Numerical computation of eigenvalues and eigenvectors of matrices

Software:

ARPACK; FFTW
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References:

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