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Is it true that unitary transform in QM corresponds to canonical transform

  1. Sep 29, 2006 #1
    Is it true that unitary transform in QM corresponds to canonical transformation in classical mechanics in this way:

    [tex]\hat{U}\Psi[O] = \Psi[O'][/tex]

    state [tex]\Psi[O][/tex] is a functional of the observable algebra, satisfying positivity and normalization conditions. [tex]O'[/tex] is the canonically transformed observable.

    what does it look like in the case of wave function [tex]\psi(x)[/tex] ???
     
    Last edited: Sep 29, 2006
  2. jcsd
  3. Sep 29, 2006 #2

    reilly

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    See Dirac's Quantum Mechanics, section 26, for a very thorough discussion of this matter. In short, Dirac notes that while unitary and contact/canonical transformations are analogous, unitary xforms are far more general than canonical ones -- QM and classical mechanics are very different.
    Regards,
    Reilly Atkinson
     
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