112 citations · 1.1k across the 124 of their papers we have counts for
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Collocation method for fractional quantum mechanics
Paolo Amore, Francisco M. Fernández, Christoph P. Hofmann +1
We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on Little Sinc Functio…
Can one hear the density of a drum? Weyl's law for inhomogeneous media
Paolo Amore
We generalize Weyl's law to inhomogeneous bodies in dimensions. Using a perturbation scheme recently obtained by us in Ref. \cite{Amore09}, we have derived an explicit formula,…
Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results
Paolo Amore
We develop powerful numerical and analytical techniques for the solution of the Helmholtz equation on general domains. We prove two theorems: the first theorem provides an exact fo…
Harmonic oscillator in a one-dimensional box
Paolo Amore, Francisco M. Fernandez
We study a harmonic molecule confined to a one--dimensional box with impenetrable walls. We explicitly consider the symmetry of the problem for the cases of different and equal mas…
Variational collocation for systems of coupled anharmonic oscillators
Paolo Amore, Francisco M. Fernandez
We have applied a collocation approach to obtain the numerical solution to the stationary Schrödinger equation for systems of coupled oscillators. The dependence of the discretized…
The virial theorem for nonlinear problems
Paolo Amore, Francisco M Fernández
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation p…
He's amazing calculations with the Ritz method
Paolo Amore, Francisco M. Fernande
We discuss an earlier application of the Ritz variational method for strongly nonlinear problems. We clearly prove that the results derived for several extremely simple problems of…