Continuous wavelet transform analysis of one-dimensional quantum bound states from first principles
- Department of Physics and Center for Theoretical Studies of Physical Systems, Clark Atlanta University, Atlanta, Georgia 30314 (United States)
Over the last decade, Handy and Bessis have developed a moment-problem-based, multiscale quantization theory, the eigenvalue moment method (EMM), which has proven effective in solving singular, strongly coupled, multidimensional Schr{umlt o}dinger Hamiltonians. We extend the scope of EMM by demonstrating its essential role in the generation of wavelet transforms for one-dimensional quantum systems. Combining this with the function-wavelet reconstruction formulas currently available, we are able to recover the wave function systematically, from first principles, through a multiscale process proceeding from large spatial scales to smaller ones. This accomplishment also addresses another outstanding problem, that of reconstructing a function from its moments. For the class of problems considered, the combined EMM-wavelet analysis yields a definitive solution. {copyright} {ital 1996 The American Physical Society.}
- OSTI ID:
- 388261
- Journal Information:
- Physical Review A, Vol. 54, Issue 5; Other Information: PBD: Nov 1996
- Country of Publication:
- United States
- Language:
- English
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