Generalized theory of semiclassical amplitudes

Citation:

Heller, E.J. Generalized theory of semiclassical amplitudes. J. Chem. Phys. 66, 5777 (1977).

Abstract:

The theory of quantum amplitudes in the semiclassical, h/→0 limit is considerably extended by including overlaps between Gaussian coherent states (wave packets) in the primitive ’’semiclassical algebra.’’ Traditionally, semiclassical formulations have exclusively involved overlaps between eigenstates of Hermitian operators; these are delocalized in most representations. Paradoxically, the states which are most localized and particlelike in the classical limit (wave packets) are not eigenfunctions of Hermitian observables, and have been omitted from asymptotic, formal theories of the semiclassical limit. When incorporated into a generalized theory, the Gaussian wave packet states apppear to alleviate many of the practical difficulties encountered in implementation of the Hermitian, delocalized state formulation. We present the generalized theory here, and show how it contains and reduces to the Hermitian semiclassical theory in various limits.

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Last updated on 10/06/2016