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Solution to the equations of the moment expansions

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Central European Journal of Physics

Abstract

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.

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References

  1. D. Horn, M. Weinstein, Phys. Rev. D 30, 1256 (1984)

    Article  ADS  Google Scholar 

  2. D. Horn, M. Karliner, M. Weinstein, Phys. Rev. D 31, 2589 (1985)

    Article  ADS  Google Scholar 

  3. J. Cioslowski, Phys. Rev. Lett. 58, 83 (1987)

    Article  ADS  Google Scholar 

  4. C. Stubbins, Phys. Rev. D 38, 1942 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  5. P. Knowles, Chem. Phys. Lett. 134, 512 (1987)

    Article  ADS  Google Scholar 

  6. P. Amore, F. M. Fernández, M. Rodriguez, J. Phys. A 44, 505302 (2011)

    Article  MathSciNet  Google Scholar 

  7. F. M. Fernández, Int. J. Quantum Chem. 109, 717 (2009)

    Article  ADS  Google Scholar 

  8. I. Bartashevich, Int. J. Quantum Chem. 108, 272 (2008)

    Article  ADS  Google Scholar 

  9. J. Cioslowski, Phys. Rev. A 36, 3441 (1987)

    Article  ADS  Google Scholar 

  10. J. Cioslowski, Chem. Phys. Lett. 136, 515 (1987)

    Article  ADS  Google Scholar 

  11. V. Fessatidis, J. D. Mancini, S. P. Bowen, M. Campuzano, J. Math. Chem. 44, 20 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Correspondence to Francisco M. Fernández.

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Amore, P., Fernández, F.M. Solution to the equations of the moment expansions. centr.eur.j.phys. 11, 195–205 (2013). https://doi.org/10.2478/s11534-012-0154-4

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  • DOI: https://doi.org/10.2478/s11534-012-0154-4

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