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Accurate calculation of the bound states of the quantum dipole problem in two dimensions

100%
Amore P.
Open Physics
|
2012
|
vol. 10
|
issue 1
96-101
EN
We present an accurate calculation of the energies of the bound states of the quantumdipole problemin two dimensions using a Rayleigh-Ritz approach. We obtain an upper bound for the energy of the ground state, which is by far the most precise in the literature for this problem. We also obtain an alternative estimate of the fundamental energy of the model performing an extrapolation of the results corresponding to different subspaces. Finally, our calculation of the energies of the first 500 states shows a perfect agreement with the expected asymptotic behavior.
2
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Solution to the equations of the moment expansions

63%
Amore P., Fernández F.
Open Physics
|
2013
|
vol. 11
|
issue 2
195-205
EN
We develop a formula for matching a Taylor series about the origin and an asymptotic exponential expansion for large values of the coordinate. We test it on the expansion of the generating functions for the moments and connected moments of the Hamiltonian operator. In the former case the formula produces the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We choose the harmonic oscillator and a strongly anharmonic oscillator as illustrative examples for numerical test. Our results reveal some features of the connected-moments expansion that were overlooked in earlier studies and applications of the approach.
3
Content available remote

High-order connected moments expansion for the Rabi Hamiltonian

51%
Amore P., Fernandez F., Rodriguez M.
Open Physics
|
2012
|
vol. 10
|
issue 1
102-108
EN
We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large-order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.
4
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Accurate calculation of the eigenvalues of non-uniform strings and membranes

51%
Amore P., Fernandez F., Rodriguez M.
Open Physics
|
2012
|
vol. 10
|
issue 4
913-925
EN
We describe a pseudospectral approach which combines a mapping procedure with the principle of minimal sensitivity to obtain accurate estimates for the eigenvalues of non-uniform strings and both uniform and nonuniform membranes. We illustrate the method on specific examples, including the case of a cross shaped membrane, with arms of infinite length.
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