Schrödinger Equation

CORE DEFINITION

In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of a physical system changes over time. It is one of the fundamental equations of quantum mechanics, named after the Austrian physicist Erwin Schrödinger, who published it. The concepts of quantum states and the Schrödinger equation are covered in the basic postulates of quantum mechanics and cannot be derived from any other principles. In classical mechanics, Newton's second law is used to describe the motion of objects. In quantum mechanics, the analogous equation of motion is the Schrödinger equation. The solutions to the Schrödinger equation completely describe the quantum behavior of microscopic particles in physical systems, including molecular, atomic, and subatomic systems. Additionally, the solutions can also completely describe macroscopic systems, possibly even the entire universe. The Schrödinger equation can be divided into two types: the time-dependent Schrödinger equation and the time-independent Schrödinger equation. The time-dependent Schrödinger equation is related to time and describes how the wave function of a quantum system evolves over time. The time-independent Schrödinger equation is independent of time and describes the physical properties of stationary quantum systems; its solutions are the wave functions of stationary quantum systems.