The time-dependent Schrödinger equation for the motion of the electron in a ${\mathrm{H}}^{+}$-H collision is solved numerically with a finite-difference method on an axially symmetric spatial mesh. Sample density distributions for $E_{\mathrm{lab}}=20\mathrm{}$ keV are shown. The calculated charge-transfer probabilities at $E_{\mathrm{lab}}=3.92, 7.69, \mathrm{and} 20.1$ keV are in good agreement with experiment.

• Received 23 May 1979

DOI:https://doi.org/10.1103/PhysRevLett.43.512