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Abstract: At any resolution level of wavelet expansions the physical observable of thekinetic energy is represented by an infinite matrix which is ``canonically-chosen as the projection of the operator $-\Delta-2$ onto the subspace of thegiven resolution. It is shown, that this canonical choice is not optimal, asthe regular grid of the basis set introduces an artificial consequence ofperiodicity, and it is only a particular member of possible operatorrepresentations. We present an explicit method of preparing a near optimalkinetic energy matrix which leads to more appropriate results in numericalwavelet based calculations. This construction works even in those cases, wherethe usual definition is unusable i.e., the derivative of the basis functionsdoes not exist. It is also shown, that building an effective kinetic energymatrix is equivalent to the renormalization of the kinetic energy by a momentumdependent effective mass compensating for artificial periodicity effects.



Autor: J. Pipek, Sz. Nagy

Fuente: https://arxiv.org/



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