Fundamental equation developed in 1926 by Erwin Schrödinger that established the mathematics of quantum mechanics .
The equation determines the behaviour of the wave function that describes the wavelike properties of a subatomic system. It relates kinetic energy and potential energy to the total energy, and it is solved to find the different energy levels of the system. Schrödinger applied the equation to the hydrogen atom and predicted many of its properties with remarkable accuracy. The equation is used extensively in atomic, nuclear, and solid-state physics. See also wave-particle duality .