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Il Nuovo Cimento (1955-1965)

, Volume 27, Issue 1, pp 261–302 | Cite as

A novel approach to elementary scattering theory

  • F. Calogero
Article

Summary

An aproach to potential scattering is discussed, which is simple, elegant and very convenient for numerical computations. The problem of evaluating scattering phase-shifts and bound-state energies is discussed. The effect of the potential on the wave function is also analysed. Approximating formulas are given. A powerful representation for the tangent of the phase shift, valid if the potential never changes sign and the phase shift is smaller in magnitude than π/2, is obtained. Bounds on the phase shifts and on their derivatives with respect to linear and angular momentum are established.

Riassunto

Si discute una formulazione della teoria della diffusione da potenziale che è semplice, elegante e molto vantaggiosa per calcoli numerici. Si discute il problema del calcolo degli sfasamenti e delle energie degli stati legati. Si analizza inoltre, l'effetto del potenziale sulla funzione d'onda. Si danno formule approssimanti gli sfasamenti. Si ottiene una notevole espressione per la tangente dello sfasamento, valida per potenziali che non cambino segno e per sfasamenti minori in modulo di π/2. Si derivano limiti superiori e inferiori per gli sfasamenti e le loro derivate rispetto all'impulso e al momento angolare.

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Copyright information

© Società Italiana di Fisica 1963

Authors and Affiliations

  • F. Calogero
    • 1
  1. 1.Department of PhysicsUniversity of CaliforniaBerkeley

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