Search results

1

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

100%

Amore P.

Open Physics

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2012

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vol. 10

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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

Solution to the equations of the moment expansions

80%

Amore P., Fernández F.

Open Physics

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2013

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vol. 11

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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

Rayleigh-Ritz variational method with suitable asymptotic behaviour

70%

Fernández F., Garcia J.

Open Physics

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2014

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vol. 12

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issue 8

554-558

EN

This paper considers the Rayleigh-Ritz variational calculations with non-orthogonal basis sets that exhibit the correct asymptotic behaviour. This approach is illustrated by constructing suitable basis sets for one-dimensional models such as the two double-well oscillators recently considered by other authors. The rate of convergence of the variational method proves to be considerably greater than the one exhibited by the recently developed orthogonal polynomial projection quantization.

4

Eigenvalues and eigenfunctions of the anharmonic oscillator V(x, y) = x 2 y 2

70%

Fernández F., Garcia J.

Open Physics

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2014

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vol. 12

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issue 7

499-502

EN

We obtain sufficiently accurate eigenvalues and eigenfunctions for the anharmonic oscillator with potential V(x, y) = x 2 y 2 by means of three different methods. Our results strongly suggest that the spectrum of this oscillator is discrete in agreement with early rigorous mathematical proofs and against a recent statement that cast doubts about it

5

Buckling analysis of composite cylindrical shells reinforced by carbon nanotubes

57%

Jam J. E., Asadi E., Jam J. E., Asadi E.

Archive of Mechanical Engineering

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2012

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vol. 59

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issue 4

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

Solution to the equations of the moment expansions

Rayleigh-Ritz variational method with suitable asymptotic behaviour

Eigenvalues and eigenfunctions of the anharmonic oscillator V(x, y) = x 2 y 2

Buckling analysis of composite cylindrical shells reinforced by carbon nanotubes