A new method for determining excited states of quantum systems
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A new method for computing excited states of a given operatorH is here presented. Our procedure is of particular value when its representation requires an orthonormal basis set of large dimension. In order to obtain the excited state ofH nearest in energy to any chosen trial energyE t, we consider the auxiliary operatorA=(H−E t)2. We show that a reasonable number of relaxations on appropriately generated low-order Krylov subspaces forA is sufficient to produce better and better approximations of its ground state; a high-accuracy final refinement of the ground state ofA is then possible through the standard Lanczos procedure. An important feature of our method is that storage memory limitations, encountered in the conventional determination of all eigenvalues of large systems, are here overcome. As an illustration of the method two significant examples are discussed.
PACS. 71.10General theories and computational techniques (including many-body perturbation theory, density-functional theory, atomic sphere approximation methods, Fourier decomposition methods, etc.)
PACS. 31.50Excited states
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