Non-adiabatic quantum evolution: The S matrix as a geometrical phase factor |
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Authors: | Y Saadi M Maamache |
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Institution: | Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Université Ferhat Abbas de Sétif, Sétif 19000, Algeria |
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Abstract: | We present a complete derivation of the exact evolution of quantum mechanics for the case when the underlying spectrum is continuous. We base our discussion on the use of the Weyl eigendifferentials. We show that a quantum system being in an eigenstate of an invariant will remain in the subspace generated by the eigenstates of the invariant, thereby acquiring a generalized non-adiabatic or Aharonov–Anandan geometric phase linked to the diagonal element of the S matrix. The modified Pöschl–Teller potential and the time-dependent linear potential are worked out as illustrations. |
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Keywords: | Non-adiabatic evolution Geometrical phase Lewis and Riesenfeld theory Scattering matrix Continuous spectrum |
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