Schrödinger equation

"Just four weeks after the first paper (Q1) the Annalen received on February 23 the second paper (Q2) in the series 'Quantization as an Eigenvalue Problem'. ... It consists of a detailed exploration of the Hamiltonian analogy between mechanics and optics leading to a new derivation of the wave equation, an analysis of the relations between security making geometrical and undulatory mechanics, and applications of the wave equation to the harmonic oscillator and the diatomic molecule."

"With the growing importance of models in statistical mechanics and in field theory, the path integral method of Feynman was soon recognized to offer frequently a more general procedure of enforcing the first quantization instead of the Schrödinger equation. To what extent the two methods are actually equivalent, has not always been understood. ... the Coulomb potential and the harmonic oscillator ... point the way: For scattering problems the path integral seems particularly convenient, whereas for the calculation of discrete security eigenvalues the Schrödinger equation."

"Interactions that look instantaneous are well suited to Schrödinger’s equation, which requires the potential between particles at equal times. It would be quite awkward to explicitly describe finite-velocity forces in the Schrödinger equation because the potential for one particle at a time t would depend on the positions of the others at the retarded times, and one would need the past histories of all the particles to propagate the system forward in time."