Solution of time-independent Schrِdinger equation by the imaginary time propagation method

Numerical solution of eigenvalues and eigenvectors of large matrices originating from discretization of linear and non-linear Schrِdinger 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.