Three different methods that are based on the coherent control of a time evolved wavefunction are used to determine the eigenvalues of Hermitian matrices. These methods are of special interest for determining eigenvalues of very large matrices and they replace the standard matrix diagonalization by a minimization problem of a few optimal time or phase variables. Upon inversion, the optimal time or phase variables directly provide the energies of higher eigenstates spanned by the initial wavefunction, without having to compute the wavefunctions themselves. The methods are applied to determine the electronic energies of the He and C atoms as well as a model harmonic oscillator system. All three methods scale as N 2 for a matrix whose dimension is N and they use as input only the overlap of the time evolved initial wavefunction with itself.View full textDownload full textKeywordstime-dependent Schrödinger equation, eigen states, stationary solutions, variational technique, optimization, coherent controlRelated var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00268976.2012.668967
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