Abstract
We present a quantum description for the evolution of atomic states of fast projectiles traveling through matter. Our approach is based on the solution of a quantum Langevin equation, i.e., a stochastic time-dependent Schr\"odinger equation that describes electronic excitations of atoms during their transport through solids. The present description can be considered the quantized version of a previously developed classical transport theory. We analyze in detail the correspondence between classical and quantum transport simulations. Applications to the stripping of relativistic ${\mathrm{H}}^{\ensuremath{-}}$ and H through thin carbon foils and a comparison with experimental data are presented.
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