FURTHER ANALYSIS OF SOLUTIONS TO THE TIME-INDEPENDENT WAVE-PACKET EQUATIONS OF QUANTUM DYNAMICS .2. SCATTERING AS A CONTINUOUS FUNCTION OF ENERGY USING FINITE, DISCRETE APPROXIMATE HAMILTONIANS
Yh. Huang et al., FURTHER ANALYSIS OF SOLUTIONS TO THE TIME-INDEPENDENT WAVE-PACKET EQUATIONS OF QUANTUM DYNAMICS .2. SCATTERING AS A CONTINUOUS FUNCTION OF ENERGY USING FINITE, DISCRETE APPROXIMATE HAMILTONIANS, The Journal of chemical physics, 105(3), 1996, pp. 927-939
We consider further how scattering information (the S-matrix) can be o
btained, as a continuous function of energy, by studying wave packet d
ynamics on a finite grid of restricted size. Solutions are expanded us
ing recursively generated basis functions for calculating Green's func
tions and the spectral density operator. These basis functions allow o
ne to construct a general solution to both the standard homogeneous Sc
hrodinger's equation and the time-independent wave packet, inhomogeneo
us Schrodinger equation, in the non-interacting region (away from the
boundaries and the interaction region) from which the scattering solut
ion obeying the desired boundary conditions can be constructed. In add
ition, we derive new expressions for a ''remainder or error term,'' wh
ich can hopefully be used to optimize the choice of grid points at whi
ch the scattering information is evaluated. Problems with reflections
at finite boundaries are dealt with using a Hamiltonian which is dampe
d in the boundary region as was done by Mandelshtam and Taylor [J. Che
m. Phys. 103, 2903 (1995)]. This enables smaller Hamiltonian matrices
to be used. The analysis and numerical methods are illustrated by appl
ication to collinear H+H-2 reactive scattering. (C) 1996 American Inst
itute of Physics.