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Quantum mechanics applies to microscopic scales (atoms and subatomic particles) and replaces classical descriptions when they fail.
Quantum mechanics (quantum physics) is the fundamental theory describing how matter and light behave at atomic and subatomic scales, where classical physics becomes insufficient. It explains phenomena such as quantized (discrete) energy and other observables, wave–particle duality, and inherent limits on prediction accuracy captured by the uncertainty principle. Although it can be applied to complex systems (e.g., molecules with many atoms), questions about measurement and interpretation can become philosophically challenging, especially when considering observers or even the universe as a whole. A central feature of quantum mechanics is its probabilistic predictions: a system’s state is represented by a wave function, and measurement outcomes are determined using probability amplitudes via the Born rule. The wave function evolves deterministically in time according to the Schrödinger equation, governed by the Hamiltonian (the total energy operator). The theory’s scope is broad: it provides mathematical formalisms for calculating properties of microscopic systems and underpins many modern fields and technologies, including quantum chemistry, quantum optics, quantum computing, and materials science.
Quantum mechanics applies to microscopic scales (atoms and subatomic particles) and replaces classical descriptions when they fail.
Physical quantities are quantized, measurement outcomes are probabilistic (Born rule), and time evolution follows the Schrödinger equation using the Hamiltonian.
The theory’s methods and concepts extend across many disciplines and enable major technologies and applications.
The fundamental physical theory describing the behavior of matter and light at atomic and subatomic scales.
A mathematical object that encodes a quantum system’s probability amplitudes for possible measurement outcomes.
The rule stating that measurement probabilities are given by the squared magnitude of probability amplitudes.
The differential equation that determines how a quantum state (wave function) evolves over time under a Hamiltonian.
The operator corresponding to the total energy of a quantum system that drives its time evolution.
A statement that certain pairs of physical quantities (e.g., position and momentum) cannot both be predicted with arbitrary precision.
The observation that quantum entities exhibit both wave-like interference and particle-like detection behavior.
The property that some observables (like energy) take discrete values in bound quantum systems rather than continuous ones.
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