The talk will be a pedagogical introduction to the use of iterative
approaches based on the time-dependent Shcroedinger equation to the
extraction of eigenvalues, eigenstates, and density matrices of linear
operators. It turns out that it is a good idea to combine time-dependent
(iterative) approaches with diagonalization methods, yielding a combined
"filter-diagonalization" method. Further, surprisingly, it turns out that
it is easy to map the problem of extracting eigenvalues and eigenstates
into the problem of signal-extraction ("harmonic-inversion") for a general
signal the method extends and is stronger than Fast-Fourier transforms.
Applications in fields as diverse as semiclassical dynamics and NMR would
be presented.
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