Wavelets and Path Integral
The matrix elements between wavelets of the quantum propagator for a large class of Hamiltonians on the half-line are given in terms of path integral. It is a sum over path defined on the upper half plane with a Wiener measure associated to the hyperbolic Laplacian in the limit where the diffusion constant diverges. The construction in the case of the circle is sketched.
KeywordsPhase Space Coherent State Half Plane Wavelet Coefficient Configuration Space
Unable to display preview. Download preview PDF.
- [2a]E. Nelson; J. Matii. Phys. 5 332 (1964)Google Scholar
- [2h]J. R. Klauder “Quantization is geometry, after all”n (Preprint AT&T BeU Laboratories, Murry Hill, NJ. 07974 USA).Google Scholar
- I. Daubechies, J. R. Klauder and T. Paul; J. Matii. Physics 28 (1987).Google Scholar
- E. Schrodinger, Sitzungsher Pniss, Akad — Wiss. Phys. Math. Klasse 906 (1930).Google Scholar
- J. R. Klauder and B. S. Skagerstam, “Coherent States, Applictions in Physics and Mathematical Physics (World Scientific, Singapore (1985).Google Scholar
- [7a]A. Grossman, J. Morlet and P. Paul and Ann. Inst. H. Poincaré 65 293 (1986).Google Scholar
- T. Paul. ThesisGoogle Scholar
- S. Graffi, T. Paul; Resonnance overlapping, quasi-energy avoided crossing and microwave ionization of hydrogen atom — preprint CPT, CNRS Luminy Case 907 13288 Marseille Cedex 9. France.Google Scholar
- J. M. Souriau “Structure des Systèmes Dynamiques” Dunod. ParisGoogle Scholar
- In preparationGoogle Scholar
- J. Bellissard; “Stability and Instability in Quantum Mechanics” in Trends and Developments in the Eighties. S. Albeveiro and P. Blanchard eds. World Scientific, 1985, Singapore.Google Scholar