Schrödinger equation

The Schrödinger equation is one of the fundamental equations of quantum mechanics and describes the spatial and temporal behavior of quantum-mechanical systems. Austrian physicist Erwin Schrödinger first proposed the equation in early 1926.

Mathematically, the Schrödinger equation is an example of an eigenvalue problem whose eigenvectors are called "wavefunctions" or "quantum states" and whose eigenvalues correspond to energy levels. Built into the eigenvectors are the probabilities of measuring all values of all physical observables, meaning that a solution of the Schrödinger equation provides a complete physical description of a (quantum) system. The Schrödinger Equation can be written in terms of Hamiltonians for as well classical systems as quantum mechanical systems. In the latter case the Hamiltonian functons are replaced by Hamiltonian operators.