On the Eigenfunctions of Many-Particle Systems in Quantum Mechanics

By Tosio Kato. 2011

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Density functional theory: Its origins, rise to prominence, and future (2015, background): “15At a conference in 1965, E. B. Wilson noted (Handy, 2009): If we know the density distribution, we can find its cusps, from which we can determine [from the electron-nucleus cusp condition (Kato, 1957)] both the location of the nuclei and their atomic numbers.”
Density functional theory: Foundations reviewed (2014, methodology): “In other words, the original reductio ad absurdum proof of the Hohenberg–Kohn theorem based on the assumption (40) is incompatible with the ad absurdum assumption (ii) since the Kato theorem is valid for such systems [268].”
Adaptive low rank wavelet methods and applications to two-electron Schrödinger equations (2012, background): “The behaviour of these cusps at two-particle coalescence points is characterized by the celebrated Kato cusp condition in terms of spherical averages.”
Low-Depth Quantum Simulation of Materials (2017, background): “Kato proved that the electronic wave function we are interested in is continuous but has a discontinuous (yet finite) first derivative at the nuclei (the electron-nuclear cusp) and at the electron-electron coincidences (the electron-electron cusp) [117].”