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An application of the gradient method to anharmonic oscillators

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Lettere al Nuovo Cimento (1971-1985)

Summary

The gradient method, introduced in previous papers as a new method for solving Schrödinger equations, is applied here to compute the first two eigen values and the corresponding eigenfunctions of the Hamiltonians H(β) =p 2 +x 2 + βx 2q, withq = 2, 3, 4 and 10-4 ≤ β ≤ 104. The results, which for smallq are excellent for all β, are compared with those obtained by other authors.

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References

  1. G. Fonte andG. Schiffrer:Nuovo Cimento B,37, 63 (1977);G. Fonte:Nuovo Cimento B,49, 200 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  2. G. Fonte andG. Schiffrer:Nuovo Cimento B,74, 1 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  3. E. K. Blum:Numerical Analysis and Computation Theory and Practice (New York, N. Y., 1972);J. Cea:Lectures on Optimization. Theory and Algorithms (Bombay, 1978). 145

  4. B. Simon:Ann. Phys. (N. Y.),58, 76 (1970).

    Article  ADS  Google Scholar 

  5. B. A. Samokish:Izv. Vyssh. Uchebn. Zaved. Mat.,5, 105 (1958).

    Google Scholar 

  6. K. Banerjee:Proc. H. Soc. London, Ser. A,364, 265 (1978).

    Article  ADS  Google Scholar 

  7. S. Graffi, V. Grecchi andB. Simon:Phys. Lett. B,32, 631 (1970);S. Graffi,V. Grecchi andG. Turchetti:Nuovo Cimento B,4, 313 (1971);M. F. Marziani:J. Phys. A, 17, 547 (1984).

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica dell’ Università, Corso Italia 57, 95129, Catania, Italia

    G. Fonte

  2. Sezione di Catania, Istituto Nazionale di Fisica Nucleare, Italia

    G. Fonte

  3. Istituto di Fisica dell’ Università, Via Paradiso 12, 44100, Ferrara, Italia

    L. Lucaroni

  4. Istituto di Fisica dell’ Università, Via Paradiso 12, 44100, Ferrara, Italia

    G. Schiffrer

  5. Sezione di Padova, Istituto Nazionale di Fisica Nucleare, Italia

    G. Schiffrer

Authors
  1. G. Fonte
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  2. L. Lucaroni
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  3. G. Schiffrer
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Additional information

Work supported by I.N.F.N., Sezione di Catania and by C.N.R. (Ferrara University contribution 81.02856.02).

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Fonte, G., Lucaroni, L. & Schiffrer, G. An application of the gradient method to anharmonic oscillators. Lett. Nuovo Cimento 43, 145–149 (1985). https://doi.org/10.1007/BF02749595

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  • DOI: https://doi.org/10.1007/BF02749595

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