Scattering of plane wave on radially symmetrical potential, in two dimensions

Computation of wavefunctions using exact quantum and semiclassical approaches

Examples of two-dimensional potentials

Click on one of the plots below
to see results of calculation		 Potential Energy Mass Short description
Morse potential from a paper of Knudson et al., 1985 Dexp[–a(r–re)] {exp[–a(r–re)]–1}D = 1ev, a = 2.5, re = 21/6 1.6 1 Morse potential from a paper of Knudson et al., 1985
Gaussian repulsive potential exp(–0.04 r2) 1.3 20 Gaussian repulsive potential
Gaussian attractive potential –exp(–0.04 r2) 0.3 20 Gaussian attractive potential
near the barrier exp(–0.04 r2) 1.001 20 near the barrier
below the barrier exp(–0.04 r2) 0.7 20 below the barrier
Gaussian multiplied by r^2 0.1 r2exp(–0.04 r2) 1 20 Gaussian multiplied by r^2
modified Gaussian, larger energy 0.1 r2exp(–0.04 r2) 2 20 modified Gaussian, larger energy
inverted modified Gaussian, larger energy –0.1 r2exp(–0.04 r2) 2 20 inverted modified Gaussian, larger energy
Gaussian repulsive potential, large energy exp(–0.04 r2) 3 20 Gaussian repulsive potential, large energy
Gaussian attractive potential, large energy –exp(–0.04 r2) 3 20 Gaussian attractive potential, large energy
Yukawa potential –exp(–0.2 r)/r 0.3 20 Yukawa potential
Oscillating Gaussian potential cos(r) exp(–0.04 r2) 2 20 Oscillating Gaussian potential
Inverted oscillating Gaussian potential –cos(r) exp(–0.04 r2) 2 20 Inverted oscillating Gaussian potential
Potential from M. Herman's notes exp(–r2) 1.3 80 Potential from M. Herman's notes
Repulsive Yukawa potential exp(–0.2 r)/r 1 20 Repulsive Yukawa potential

Mathematica programs