Schrödinger's equation is a fundamental equation in quantum mechanics that describes the behavior of quantum particles through wavefunctions. The equation is named after Austrian physicist Erwin Schrödinger, who developed it in 1926.

In simple terms, the equation is used to calculate the probability distribution of a particle's position or momentum at any given time. The wavefunction, denoted by the Greek letter Psi (Ψ), represents the state of the particle and contains all the information about its quantized energy levels and possible states.

For example, let's consider an electron confined within a one-dimensional box. The wavefunction of the electron can be represented by a mathematical function, such as Ψ(x), which describes the probability of finding the electron at a particular position along the box.

The behavior of quantum particles governed by Schrödinger's equation is different from classical particles, which follow deterministic laws. Quantum particles exist in a superposition of states, meaning they can exist in multiple states simultaneously until measured. This concept is known as wave-particle duality and is a cornerstone of quantum mechanics.

Tags: quantum mechanics, Schrödinger's equation, wavefunctions