21. Time-dependent Schrodinger equation

The Schrodinger equation, the basis of quantum mechanics, was discovered by Erwin Schrodinger during his skiing holiday at the end of 1925 and analyzed by him in a series of papers published in Annalen der Physik in 1926. By the end of that year, the face of physics had changed. Schrodinger won the Nobel Prize in Physics in 1933. For a system of N particles in three dimensions, the Schrodinger equation applies in a state space of dimension 3N. However, let us consider the familiar case of a single point particle, so that the state space is IR 3. Suppose the particle has mass m and is subject to a force F (r) = rV (r), where V (r) is a xed potential function. For example, the particle might be an electron attracted to a proton at r = 0 by an inverse square force with V (r) = C=jrj (the hydrogen atom). A physicist would write the equation as i