SMF

Long range scattering and the Stark effect

Long range scattering and the Stark effect

Denis WHITE
  • Année : 1992
  • Tome : 210
  • Format : Papier, Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 35P25, 47A40, 81U05
  • Pages : 341-353
  • DOI : 10.24033/ast.196

We prove the completeness of Dollard's modified wave operators for the Stark effect Hamiltonians $H_0 = -(1/2)\Delta - x_1$ and $H = H_0 + V$ where $V$ is a general long range potential. As a consequence, the “unmodified” wave operators do not exist if $V$ is not short range. In one space dimension this quantum mechanical result differs from the ical result : Jensen and Ozawa have shown that the usual wave operators in ical mechanics do exist. We show however that his mathematical difference cannot be detected by any quantum mechanical observable. We derive the existence and completeness of the modified wave operators (in arbitrary space dimensions) from the comparable result for two Hilbert space wave operators by a stationary phase argument.

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