  Recent advances in machine learning establish the ability of certain
neural-network architectures called neural operators to approximate maps
between function spaces. Motivated by a prospect of employing them in
fundamental physics, we examine applications to scattering processes in quantum
mechanics. We use an iterated variant of Fourier neural operators to learn the
physics of Schr\"odinger operators, which map from the space of initial wave
functions and potentials to the final wave functions. These deep operator
learning ideas are put to test in two concrete problems: a neural operator
predicting the time evolution of a wave packet scattering off a central
potential in $1+1$ dimensions, and the double-slit experiment in $2+1$
dimensions. At inference, neural operators can become orders of magnitude more
efficient compared to traditional finite-difference solvers.
