Electron energy spectra obtained from the quantum and classical models for the following set of parameters: , , , . (a) Spectrum obtained with the ADI method for (solid line) and (dotted line); (b) the same spectrum obtained with the spectral method for (solid line) and (dotted line). The thick dashed (thin dash-dotted) line in panel (b) shows the result of the classical dynamical model for . The dashed line in panel (a) shows the result of the classical model of instantaneous collisions. Also shown for comparison is the energy spectrum of the electron in the ground state of hydrogen (dotted-dashed line).
Influence of the parameter (thick dash-dotted line), (thick dashed line), and (thin dotted line) on the cutoff energy in classical model simulations. The solid curve presents the distribution obtained from the quantum calculation. The parameters are the same as in Fig. 1.
Energy spectrum (11) (a) and momentum spectrum (b) of scattered electrons for the incident velocity , for (solid line) and (dashed line). Other parameters are the same as in Fig. 1. The TDSE is solved with the ADI method.
(Color) Position of particles at the end of classical calculations sent within the certain range of impact parameters: red, ; yellow, ; green, ; blue, . The parameters are the same as in Fig. 1.
Momentum distribution of scattered particles in the propagation direction for the quantum calculations for (solid line) and (dashed line). The parameters are the same as in Fig. 1. The TDSE is solved with the spectral method.
(Color) Probability density distributions of (a) momentum and (b) position of the scattered particle for the incident velocity . Probability decreases on a logarithmic scale from red to blue. The potential is repulsive and other parameters are the same as in Fig. 1. The TDSE is solved with the ADI method.
Characteristic parameters of the calculations and the accelerated electrons for the electron scattering on the attractive and repulsive charge; a comparison between the quantum-mechanical (qm) and classical (cl) calculations and the theoretical (th) formula (15).
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