Moment-wavelet quantization and (complex) multiple turning point contributions

Wavelet transform theory is an efficient multiscale formalism for analysing local structures. This philosophy, when incorporated within quantum mechan ics, demands that there be a naturally corresponding, localized quantizatio n theory, in contrast to the variational formalisms in the literature. Thro ugh the recently established equivalency formalism between moment quantizat ion theory and continuous wavelet transform theory (Handy C R and Murenzi R 1998 J. Phys. A: Math. Gen. 31 9897 and Handy C R and Murenzi R 1999 J. Ph ys. A: Math. Gen. 32 8111), we argue that a new quantization prescription c an be defined in which the kinetic energy termis set to zero at the (comple x) turning points (or turning hypersurfaces). We establish this, both For o ne- and two-dimensional systems, and clarify the relevancy of multiscale wa velet analysis in this quantization process.