Quantum mechanics

Quantum theory developed in the early twentieth century when classical physics could not correctly account for observations such as the spectrum of thermal radiation and the photoelectric effect. In 1900, Max Planck proposed that radiation energy is emitted in discrete packets, later called quanta. Albert Einstein applied the idea of light quanta to the photoelectric effect. In 1925 Werner Heisenberg developed matrix mechanics, and in 1926 Erwin Schrödinger formulated wave mechanics; these mathematically different approaches were shown to make equivalent predictions. Max Born's probability interpretation gave the wave function a central role in predicting measurement outcomes.

A quantum system is described by a state, often represented in introductory treatments by a wave function. The wave function is not a directly observable path through space; under the Born rule, its squared magnitude gives probability density for possible position measurements. Quantum mechanics can therefore predict the statistical distribution of outcomes for repeated preparations, even when it does not specify a single certain result for each measurement. The Schrödinger equation describes how a system's state changes with time in many nonrelativistic settings.

Quantization means that certain observables in a system, such as the energy levels of an electron bound in an atom, take only particular allowed values. Quantum objects also display wave-like and particle-like behavior in different experimental contexts. A system can be in a superposition of states, which can produce interference among possible outcomes. The uncertainty principle places a fundamental limit on how narrowly certain pairs of properties, such as position and momentum, can be specified together; it is not simply a shortcoming of measuring instruments. Entanglement is a shared quantum state of multiple systems that produces correlations unlike those predicted by classical local models. Experiments testing Bell inequalities have confirmed such correlations; they do not provide a way to send controllable messages faster than light.

Quantum mechanics explains the structure of atoms and molecules and is essential to understanding many material properties. The theory is used in the science behind semiconductor devices, lasers and atomic clocks; the accurate timing of atomic clocks supports systems such as satellite navigation. Quantum theory is exceptionally successful at predicting experimental results, but physicists and philosophers continue to debate what the mathematical state represents and how to understand measurement. Different interpretations seek to explain the same established formal predictions, and ongoing experiments test the theory's consequences and explore new quantum technologies.