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Il Nuovo Cimento B (1971-1996)

, Volume 74, Issue 1, pp 1–26 | Cite as

On the gradient method in quantum mechanics

  • G. Fonte
  • G. Schiffrer
Article

Summary

We present the gradient method as a numerical procedure for the discrete spectrum of Hamiltonian operators in a version which is more general and has better numerical flexibility than a previous version. We show that the gradient method, in addition to have relationships to the Rayleigh-Schrödinger perturbation theory and to the variational method, has also some advantageous features in comparison with them and even in comparison with the Padé and Borel summability methods. In order to check the numerical efficiency of our procedure, we have applied it, with encouraging results, to the calculation of the ground-state energy of the anharmonic oscillatorsp2+x2+βx4 andp2+x2+βx8 for a large range of β.

PACS. 03.65

Quantum theory quantum mechanics 

Riassunto

Si presenta il metodo del gradiente come procedimento numerico per lo spettro discreto di operatori hamiltoniani in una versione che è piú generale ed ha una migliore flessibilità numerica di una precedente versione. Si mostra che il metodo del gradiente, oltre ad avere connessioni con la teoria perturbativa di Rayleigh-Schrödinger e col metodo variazionale, ha anche vantaggi su questi e perfino sui metodi di sommabilità di Padé e Borel. Al fine di provare l’efficienza numerica del procedimento, questo è stato applicato, con risultati incoraggianti, al calcolo dell’energia dello stato fondamentale degli oscillatori anarmonicip2+x2+βx4 ep2+x2+βx8 per un largo intervallo di β.

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Copyright information

© Società Italiana di Fisica 1983

Authors and Affiliations

  • G. Fonte
    • 1
    • 2
  • G. Schiffrer
    • 3
    • 4
  1. 1.Istituto di Fisica Teorica dell’UniversitàCataniaItalia
  2. 2.Istituto Nazionale di Fisica NucleareSezione di CataniaCataniaItalia
  3. 3.Istituto di Fisica dell’UniversitàFerraraItalia
  4. 4.Istituto Nazionale di Fisica NucleareSezione di PadovaPadovaItalia

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