Quantum mechanics describes a quantum system using a quantum state, with observables represented by self-adjoint operators. For a single particle in one dimension, a pure state can be described by a wavefunction : its squared modulus gives the probability density for position. The Schrödinger equation predicts how this probability amplitude evolves between interventions; measurement in quantum mechanics connects it to experimental outcomes through the Born rule. A wavefunction therefore predicts a distribution of possible positions rather than a single trajectory as in classical mechanics.
The infinite square well makes three central ideas visible with elementary sine functions. Confinement selects discrete energy eigenvalues; wavefunction normalization converts a shape into quantitative probabilities; and a quantum superposition can have a changing probability density even when each constituent energy eigenstate has a stationary one. This combination explains why quantum mechanics uses both linear algebra and differential equations: eigenfunctions describe the building blocks, while quantum phases determine how they interfere. The same tools help explain the discrete energies of chemical atoms and molecules, although their Quantum Hamiltonians require different potentials and often many particles.
In his first 1926 paper, Erwin Schrödinger formulated quantization as an eigenvalue problem for a hydrogen atom in nonrelativistic quantum mechanics. On its opening page he compared the emergence of integers with the number of nodes of a standing wave on a vibrating string. The infinite square well below realizes that appealing idea especially transparently: the allowed integers follow from the boundary conditions. This historical analogy concerns the origin of discrete energies; the Born rule supplies the statistical interpretation of the modern wavefunction. [ref]
Quantisierung als Eigenwertproblem (Erste Mitteilung) by Erwin Schrödinger. Schrödinger, Quantisierung als Eigenwertproblem, 1926, pp. 361–363
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Physicist whose work includes the stabilizer formalism for quantum error correction. His The Heisenberg Representation of Quantum Computers by Daniel Gottesman develops the Pauli group description of Clifford circuits. Verified institutional profile.
Daniel Gottesman. External portrait supplied by the University of Maryland Department of Computer Science; photographer and licence are not specified on the verified profile.
Source. 
Portrait of Avshalom Elitzur
. Avishag Shaar-Yashuv. CC BY-SA 4.0, via Wikimedia Commons. Source.A physicist who proposed a unitary relative-state account of quantum measurement, developed in the many-worlds interpretation.
Hugh Everett III in 1964; Hugh Everett III papers, University of California, Irvine; photographer unrecorded in the Wikimedia file record; non-free historical portrait hosted by English Wikipedia
. Source. Coauthor of the Pusey-Barrett-Rudolph theorem.
Coauthor of the Pusey-Barrett-Rudolph theorem.
Coauthor of the Pusey-Barrett-Rudolph theorem.
Coauthor of an ontological model of a quantum system classification distinguishing psi-ontic models and psi-epistemic models.
Coauthor of an ontological model of a quantum system classification distinguishing psi-ontic models and psi-epistemic models.
Portrait of Detlef Dürr
. Via Wikimedia Commons; credits and usage information are on the linked source file page. Source.Coauthor of the original Ghirardi-Rimini-Weber theory.
Coauthor of the original Ghirardi-Rimini-Weber theory.
Coauthor of the original Ghirardi-Rimini-Weber theory and work on its interpretation.
Author of the 1964 Bell theorem argument.
Portrait of John Stewart Bell
. CERN, portrait of John Bell, June 1982; CERN archive record 1823937. CC BY 4.0, via Wikimedia Commons. Source.A physicist who coauthored a 2022 experimental demonstration of programmable neutral-atom quantum algorithms and multipartite entanglement using Rydberg blockade.
Portrait of Michael Berry (physicist)
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Portrait of Peter Zoller
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Portrait of Ignacio Cirac
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Portrait of Charles H. Bennett
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Lucien Hardy; portrait hosted by Perimeter Institute
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Portrait of Martin Bodo Plenio
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Portrait of Lev Vaidman
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Portrait of David Albert
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Portrait of Michael Nielsen
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Portrait of Boris Podolsky
. Photographer unknown. Historical identification portrait hosted by English Wikipedia as non-free media; see the linked file page for its source and copyright information. Source.A physicist who developed matrix mechanics and held a professorship in theoretical physics at Hamburg.[ref]
Jordan, Pascual (1902–1980). Bezug zu Hamburg: theoretical physics professor; Lebenslauf: full name and 1902–1980 dates
Portrait of Pascual Jordan
. Unknown photographer; Mondadori Publishers. Public domain (anonymous historical photograph, as declared on Commons). Source and usage information on the linked Wikimedia file page. Source.A physicist, Professor of theoretical physics at Birkbeck from 1961 to 1987.[ref]
Archives and special collections. The David Bohm Papers: Professor of Theoretical Physics, 1961–1987
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Portrait of David Bohm
. Unknown photographer; crop credited to Commons contributor JB Hoang Tam. Attribution-only permission, as declared on the Commons file record; no Creative Commons licence is asserted., via Wikimedia Commons. Source.A physicist researching quantum theory and the Aharonov-Bohm effect.[ref]
Dr. Yakir Aharonov. Biography: professor of theoretical physics; Institute for Quantum Studies directorship
Portrait of Yakir Aharonov
. Kobi Kalmanovitz (קובי קלמנוביץ), as credited in the Hebrew File record; EMET Prize website. Creative Commons Attribution-Share Alike 3.0 Unported., via Wikimedia Commons. Source.A physicist researching quantum optics and quantum foundations.[ref]
Professional profile of Anton Zeilinger (oeaw.ac.at). Forschungsbereiche.
Portrait of Anton Zeilinger
. CEU / Daniel Vegel; George Yul, existing portrait crop. CC BY 2.0, via Wikimedia Commons. Source.A physicist who holds an experimental quantum-physics chair at LMU Munich.[ref]
Professional profile of Harald Weinfurter (lmu.de). Final biographical paragraph explicitly names experimental quantum physics chair.
Portrait of Harald Weinfurter
. External portrait hosted by LMU Munich, Experimental Quantum Physics. Source.
Portrait of Dirk Bouwmeester in 2014
. Image from the Netherlands Organisation for Scientific Research, via Wikimedia Commons; the linked file page provides photographer credits and usage information. Source.A physicist researching quantum optics and quantum information science.[ref]
Professional profile of Dirk Bouwmeester (universiteitleiden.nl). Opening paragraph; Academic staff.
A physicist researching experimental quantum information science.[ref]
Professional profile of Jian-Wei Pan (quantum.ustc.edu.cn). Introduction; research-focus paragraph.
Portrait of Pan Jianwei
. Uuongkinghe. CC BY-SA 4.0, via Wikimedia Commons. Source.A physicist researching quantum optics and the foundations of quantum mechanics.[ref]
Professional profile of Alain Aspect (academie-sciences.fr). Biographie, first two paragraphs.
Portrait of Alain Aspect
. École polytechnique Université Paris-Saclay; Adem, existing portrait crop. CC BY-SA 2.0, via Wikimedia Commons. Source.A physicist who performed experimental tests of Bell inequalities.[ref]
Professional profile of John Francis Clauser (johnclauser.com). Self-authored opening identity paragraph.
Portrait of John Clauser
. Peter Lyons, photograph; Adem, existing portrait crop. CC BY-SA 4.0, via Wikimedia Commons. Source.A physicist who researched nuclear physics and experimentally tested Bell inequalities.[ref]
Professional profile of Stuart Jay Freedman (newscenter.lbl.gov). Opening biography; final biographical paragraphs.
Portrait of Stuart Freedman
. Lawrence Berkeley National Laboratory (Commons author field and photoarchive source). CC BY-SA 4.0, via Wikimedia Commons. Source.A physicist.[ref]
https://physics.yale.edu/profile/ramamurti-shankar. Independent professional profile
Portrait of Ramamurti Shankar
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Portrait of Wolfgang Pauli
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Portrait of Werner Heisenberg
. Source. Theoretical physics.[ref]
https://archives.collections.ed.ac.uk/repositories/2/archival_objects/237297. Independent professional profile
Portrait of Louis de Broglie
. Agence Rol; Bibliothèque nationale de France, département Estampes et photographie, EI-13 (1675), Rol 142233. Commons records public-domain status in France for this historical agency photograph and in the United States for pre-1931 publication; mechanical scan marked PD-scan. Other jurisdictions may differ., via Wikimedia Commons. Source. Articles were limited to the first 100 out of 1292 total.
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This is a section about Quantum mechanics!
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Quantum mechanics is a fundamental branch of physics that deals with the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles. It departs significantly from classical mechanics, which describes the motion of macroscopic objects. Here are some key principles and concepts of quantum mechanics: 1. **Wave-Particle Duality**: Particles, such as electrons and photons, exhibit both wave-like and particle-like properties.
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Quantum mechanics is quite a broad term. Perhaps it is best to start approaching it from the division into:
- non-relativistic quantum mechanics: obviously the simpler one, and where you should start
- relativistic quantum mechanics: more advanced, and arguably "less useful"
Key experiments that could not work without quantum mechanics: Section "Quantum mechanics experiment".
Mathematics: there are a few models of increasing precision which could all be called "quantum mechanics":
Ciro Santilli feels that the largest technological revolutions since the 1950's have been quantum related, and will continue to be for a while, from deeper understanding of chemistry and materials to quantum computing, understanding and controlling quantum systems is where the most interesting frontier of technology lies.