Tosio Kato's Work on Non--Relativistic Quantum Mechanics

We review the work of Tosio Kato on the mathematics of non–relativistic quantum mechanics and some of the research that was motivated by this. Topics include analytic and asymptotic eigenvalue perturbation theory, Temple–Kato inequality, self–adjointness results, quadratic forms including monotone convergence theorems, absence of embedded eigenvalues, trace class scattering, Kato smoothness, the quantum adiabatic theorem and Kato’s ultimate Trotter Product Formula.