CONTRACTED DISTRIBUTED APPROXIMATING FUNCTIONS - DERIVATION OF NONOSCILLATORY FREE PARTICLE AND HARMONIC PROPAGATORS FOR FEYNMAN PATH INTEGRATION IN REAL-TIME

Contracted continuous distributed approximating functions (CCDAFs) hav e been developed. In particular, it has been shown that, continuous di stributed approximating functions (CDAFs) based on standard orthogonal polynomials can be contracted to functions formed as the product of a weight function and the sine function or a Bessel function of the fir st kind. The CCDAFs of Hermite type have been applied to derive new ex pressions for the coordinate representation of the free particle evolu tion operator and that of the evolution operator of harmonic oscillato r. These new expressions of free particle and harmonic propagators hav e as compact mathematical form as Makri's effective free propagator [N . Makri, Chem. Phys. Lett. 159, 489 (1989)] and Gaussian decay identic al to that of the CDAF class free and harmonic propagators due to Kour i et al. [D. J. Kouri, W. Zhu, X. Ma, B. M. Pettitt, and D. K. Hoffman , J. Phys. Chem. 96, 9622 (1992)] and Marchioro et al: [T. L. Marchior o III M. Arnold, D. K. Hoffman, W. Zhu, Y. Huang, and D. J. Kouri, Phy s. Rev. E50, 2320 (1994)], respectively. The Gaussian decay of a CCDAF Hermite free propagator has been shown to be the result of including momentum eigenstates in the propagator which have momenta larger than the momentum of the wave packet of largest momentum that still can be well approximated by the CCDAF considered. (C) 1998 American Institute of Physics.