Renormalized semiclassical quantization for rescalable Hamiltonians
- Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, 153-8902, Tokyo (Japan)
A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum.
- OSTI ID:
- 20646161
- Journal Information:
- Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
- Country of Publication:
- United States
- Language:
- English
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