This paper serves as a first-time report on formulating important aspects of electronic spectroscopy and quantum dynamics in condensed harmonic systems using the framework of wavelets, and a stepping stone to our future work on developing anharmonic wavelets. The Morlet wavelet is taken to be the mother wavelet for the initial state of the system of interest. This work reports daughter wavelets that may be used to study spectroscopy and dynamics of harmonic systems. These wavelets are shown to arise naturally upon optical electronic transition of the system of interest. Natural birth of basis (daughter) wavelets emerging on exciting an electronic two-level system coupled, both linearly and quadratically, to harmonic phonons is discussed. It is shown that this takes place through using the unitary dilation and translation operators, which happen to be part of the time evolution operator of the final electronic state. The corresponding optical autocorrelation function and linear absorption spectra are calculated to test the applicability and correctness of the herein results. The link between basis wavelets and the Liouville space generating function is established. An anharmonic mother wavelet is also proposed in the case of anharmonic electron-phonon coupling. A brief description of deriving anharmonic wavelets and the corresponding anharmonic Liouville space generating function is explored. In conclusion, a mother wavelet (be it harmonic or anharmonic) which accounts for Duschinsky mixing is suggested.
|Journal||Journal of Physics B: Atomic, Molecular and Optical Physics|
|Publication status||Published - Mar 28 2013|
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics