# Schrodingers equation

**Schrodingers equation** is a **linear partial differential equation** that describes the wave function or state function of a quantum-mechanical system. ^{} It is a key result in **quantum mechanics**, and its discovery was a significant landmark in the development of the subject. The equation is named after **Erwin Schrödinger**, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his **Nobel Prize in Physics** in 1933.^{}^{}

In **classical mechanics, Newton’s second law** (**F** = *m***a**) ^{} is used to make a mathematical prediction as to what path a given physical system will take over time following a set of known initial conditions. Solving this **equation** of Schrodingers equation gives the position and the momentum of the physical system as a function of the external force {\displaystyle \mathbf {F} } on the system. Those two parameters are sufficient to describe its state at each time instant. In quantum mechanics, the analogue of Newton’s law is Schrödinger’s equation.

## The mechanics of Schrodingers equation

The concept of a wave function is a fundamental **postulate of quantum mechanics**; the wave function defines the state of the system at each spatial position, and time. Using these postulates, Schrödinger’s equation can be derived from the fact that the time-evolution operator must be **unitary**, and must therefore be generated by the exponential of a **self-adjoint operator**, which is the quantum Hamiltonian. This derivation is explained below.

In the **Copenhagen interpretation** of quantum mechanics, the wave function is the most complete description that can be given of a physical system. Solutions to Schrödinger’s equation describe not only molecular, atomic, and **subatomic **systems, but also **macroscopic systems**, possibly even the whole universe. ^{} Schrödinger’s equation is central to all applications of quantum mechanics, including **quantum field theory**, which combines special relativity with quantum mechanics. Theories of quantum gravity, such as **string theory**, also do not modify Schrödinger’s equation.

The Schrödinger equation is not the only way to study quantum mechanical systems and make predictions. The other formulations of quantum mechanics include **matrix mechanics**, introduced by **Werner Heisenberg**, and the **path integral formulation**, developed chiefly by Richard Feynman. **Paul Dirac** incorporated matrix mechanics and the Schrödinger equation into a single formulation.

Source: Wikipedia

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