2013
DOI: 10.1063/1.4821126
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Solving the Schrödinger eigenvalue problem by the imaginary time propagation technique using splitting methods with complex coefficients

Abstract: The Schrödinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional time steps of order greater than two necessarily have negative steps and cannot be used for this class of diffusive problems. However, there exist methods which use fractional complex time steps with positive real parts which can be used with only a moderate increase in the computational cost. W… Show more

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Cited by 69 publications
(92 citation statements)
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“…the semigroup dynamics exp(−tH/ ) with t ≥ 0 that particularly matters, [18,19]. This, in view of obvious domain and convergence/regularization properties which are implicit in the Euclidean/statistical (e.g.…”
Section: Solution Of the Schrödinger Eigenvalue Problem By Means mentioning
confidence: 99%
See 3 more Smart Citations
“…the semigroup dynamics exp(−tH/ ) with t ≥ 0 that particularly matters, [18,19]. This, in view of obvious domain and convergence/regularization properties which are implicit in the Euclidean/statistical (e.g.…”
Section: Solution Of the Schrödinger Eigenvalue Problem By Means mentioning
confidence: 99%
“….. The latter restriction may be lifted, since it is known how to handle degenerate spectral problems, [18,19].…”
Section: Solution Of the Schrödinger Eigenvalue Problem By Means mentioning
confidence: 99%
See 2 more Smart Citations
“…As for standard splitting methods, this order barrier can be circumvented if the coefficients are allowed to be complex-valued. In [2], Bader et al derive several high order forcegradient schemes with complex coefficients with positive real parts, suitable for parabolic problems.…”
Section: Introductionmentioning
confidence: 99%