Schrödingeregyenletre

Schrödinger's equation is a fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes over time. It was formulated by Austrian physicist Erwin Schrödinger in 1926. The equation exists in two main forms: the time-dependent Schrödinger equation and the time-independent Schrödinger equation.

The time-dependent Schrödinger equation is a partial differential equation that relates the wave function of a system to its potential energy and total energy. The wave function, often denoted by the Greek letter psi (Ψ), is a mathematical function that contains all the probabilistic information about the system. The square of the magnitude of the wave function at a particular point in space and time gives the probability density of finding the particle at that location and time.

The time-independent Schrödinger equation is used to find the stationary states of a quantum system, which are states where the probability distribution does not change over time, even though the wave function itself might evolve with a constant frequency. This equation is particularly useful for determining the energy levels of atoms and molecules, as well as the behavior of electrons in solids.

Schrödinger's equation is a cornerstone of quantum physics, providing the mathematical framework for understanding phenomena at the atomic and subatomic levels, such as wave-particle duality, quantization of energy, and quantum tunneling. Its predictions have been extensively verified by experiments.