Quantum mechanics is a fundamental theory of physics governing matter and radiation at atomic and subatomic scales, formulated in the 1900s to explain phenomena such as blackbody radiation, the photoelectric effect, atomic spectra, and chemical bonding; it departs from classical determinism by describing measurement outcomes with probabilities encoded in a wave function. According to Encyclopaedia Britannica, the theory accounts for discrete (quantized) energies, wave–particle duality, and uncertainty, and has been tested with extraordinary precision across atomic and condensed-matter systems. (Britannica: Quantum mechanics). (
britannica.com)
Historical development
- –In 1900, Max Planck introduced energy quanta to resolve blackbody radiation, inaugurating the quantum hypothesis; the Nobel Foundation summarizes that Planck’s proposal, characterized by Planck’s constant h, solved the ultraviolet catastrophe.
(NobelPrize.org: Planck 1918 facts). (
- –In 1905, Albert Einstein explained the photoelectric effect by proposing light quanta (photons), earning the 1921 Nobel Prize; Britannica details the frequency dependence of electron kinetic energy and instantaneous emission that classical waves could not explain.
(Britannica: Photoelectric effect);
- –In 1913, Niels Bohr applied quantization to atomic orbits to explain hydrogen spectra, laying groundwork later superseded by full quantum mechanics.
- –In 1925, Werner Heisenberg introduced matrix mechanics; in 1926, Erwin Schrödinger formulated wave mechanics and the Schrödinger equation, shown to be equivalent to Heisenberg’s approach. Britannica outlines the Schrödinger equation’s role in predicting atomic structure.
- –Heisenberg’s uncertainty principle (1927) formalized intrinsic limits on simultaneous knowledge of conjugate variables (e.g., position and momentum), a hallmark of the theory.
- –Max Born proposed the probabilistic interpretation (Born rule) of the wave function in 1926, identifying |ψ|² as a probability density for measurement outcomes. [(Born, 1926; journal reference)](journal://Zeitschrift für Physik|Zur Quantenmechanik der Stößvorgänge|1926); see overview
(Born rule). (
- –Paul A. M. Dirac unified quantum mechanics with special relativity via the Dirac equation (1928), predicting electron spin and antimatter; the American Physical Society’s “Quantum Milestones” recounts its impact.
(APS Physics: Quantum Milestones—Dirac equation). (
Mathematical formalism
Standard (nonrelativistic) quantum mechanics represents physical systems by state vectors (or density operators) in a complex Hilbert space; observables correspond to self-adjoint operators whose eigenvalues give possible measurement results; dynamics are generated by the Hamiltonian via the Schrödinger equation; and noncommuting observables satisfy canonical commutation relations (e.g., x, p = iℏ). The Stanford Encyclopedia of Philosophy succinctly summarizes these axioms, including the Hilbert-space state postulate, operator observables, and unitary time evolution. (SEP: Quantum Mechanics). (
plato.stanford.edu)
Von Neumann provided a rigorous operator-algebraic foundation (spectral theory, projection-valued measures) in 1932, and Dirac’s bra–ket calculus remains standard in practice. [(book: von Neumann, 1932)](book://John von Neumann|Mathematical Foundations of Quantum Mechanics|Springer|1932); [(book: Dirac, 1930)](book://P. A. M. Dirac|The Principles of Quantum Mechanics|Oxford University Press|1930); see Britannica’s treatments of commutation and uncertainty for core relations. (Britannica: Quantum mechanics—Heisenberg uncertainty principle). (
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Core phenomena and experiments
- –Wave–particle duality and interference: Single-particle interference has been directly visualized for electrons and photons, with fringes building up one detection at a time; Physics World and AJP describe modern double-slit demonstrations.
(Physics World: Double-slit experiment);
(American Journal of Physics, 2024). (
- –Spin and quantization: The 1922 Stern–Gerlach experiment revealed discrete angular-momentum projections (space quantization), a cornerstone of spin physics.
- –Tunneling: Quantum mechanical barrier penetration explains α-decay and underlies devices such as the scanning tunneling microscope.
- –Entanglement and nonlocal correlations: Bell’s theorem (1964) shows that no local hidden-variable theory reproduces all quantum predictions; early and subsequent experiments (Freedman–Clauser 1972; Aspect 1980s; later long-distance tests) violated Bell inequalities, culminating in the 2022 Nobel Prize to Aspect, Clauser, and Zeilinger.
(APS: Bell 1964);
Interpretations and the measurement problem
Quantum mechanics’ statistical algorithm is unambiguous, yet accounts of what the formalism “says” about reality diverge. The Copenhagen interpretation—shaped by Niels Bohr and Werner Heisenberg—emphasizes complementarity and the contextual role of measurement, while formal alternatives include Bohmian mechanics (pilot-wave), many-worlds (Everettian), and collapse models. Britannica explains Bohr’s complementarity; SEP overviews the formal core and links to treatments of the measurement problem and rival interpretations. (Britannica: Complementarity principle);
(SEP: Quantum Mechanics); see archived SEP entry on measurement.
(SEP: Measurement in quantum theory, archive). (
britannica.com)
Decoherence theory explains the practical emergence of classical outcomes by environment-induced suppression of interference between pointer states, clarifying why superpositions appear as mixtures for macroscopic apparatus. Zurek’s comprehensive review in Reviews of Modern Physics surveys einselection and redundancy (quantum Darwinism). (RMP 2003: Zurek). (
ui.adsabs.harvard.edu)
Extensions and unifications
Relativistic and many-body regimes are described by quantum field theory (QFT), which treats particles as excitations of fields; quantum electrodynamics (QED) achieves some of the most precise predictions in science (e.g., lepton magnetic moments and Lamb shift), and is a template for the Standard Model’s gauge theories. Britannica surveys QFT and QED’s precision. (Britannica: Quantum field theory);
(Britannica: Quantum electrodynamics). (
britannica.com)
Applications and technologies
Quantum mechanics underlies semiconductors, lasers, magnetic resonance, superconductivity (including Josephson effects), and emerging quantum information science. Britannica outlines these applications, and its overview of quantum computing describes qubits, superposition, entanglement, decoherence, and error correction challenges. (Britannica: Quantum mechanics—overview of impact);
(Britannica: How do quantum computers work?);
(Britannica: Josephson effect). (
britannica.com)
Key equations and postulates (nonrelativistic)
- –Schrödinger equation iℏ∂t|ψ⟩ = Ĥ|ψ⟩ for unitary time evolution.
- –Canonical commutation x, p = iℏ and general operator algebra on Hilbert space.
(SEP: Quantum Mechanics). (
- –Born rule: measurement probabilities P = |⟨a|ψ⟩|². [(Born, 1926; journal reference)](journal://Zeitschrift für Physik|Zur Quantenmechanik der Stößvorgänge|1926).
- –Projection/POVM postulates for measurement and density matrices for mixed states.