ISSN:
1573-9333
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Conclusions We have shown that good separability of the Hamiltonian in time, i.e.,τ γ -separability, is sufficient to formulate time-dependent scattering theory. The property ofτ γ -separability, extended to all the operators of Galileo or Poincaré transformations, guarantees corresponding invariance of the scattering operators. From the structure of these groups we have used only the adiabaticity (16) of the Galileo and Poincaré transformations, this being equivalent to the presence in these groups of an invariant Abelian subgroup containing taining time translations. Therefore, adiabaticity in conjunction withτ γ -separability can serve as the basis for the quantum definition of a group of motion transformations compatible with the given Hamiltonian. It can be seen from the paper that in the case when the main prescribed entity is the evolution operator Ut, separability in time plays a more fundamental role than separability in space. Moreover, for the Galileo and Poincaré groups, separability of the scattering operators under spatial transformations is a consequence of separability of the motion transformation operators in time.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01041676
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