Wave function collapse information

In quantum mechanics, wave function collapse, also called reduction of the state vector,^[1] occurs when a wave function—initially in a superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is called an observation, and is the essence of a measurement in quantum mechanics, which connects the wave function with classical observables such as position and momentum. Collapse is one of the two processes by which quantum systems evolve in time; the other is the continuous evolution governed by the Schrödinger equation.^[2]

Calculations of quantum decoherence show that when a quantum system interacts with the environment, the superpositions apparently reduce to mixtures of classical alternatives. Significantly, the combined wave function of the system and environment continue to obey the Schrödinger equation throughout this apparent collapse.^[3] More importantly, this is not enough to explain actual wave function collapse, as decoherence does not reduce it to a single eigenstate.^[4]^[5]

Historically, Werner Heisenberg was the first to use the idea of wave function reduction to explain quantum measurement.^[6] ^{[citation needed]}

^ Penrose, Roger (May 1996). "On Gravity's role in Quantum State Reduction". General Relativity and Gravitation. 28 (5): 581–600. doi:10.1007/BF02105068. ISSN 0001-7701.
^ J. von Neumann (1932). Mathematische Grundlagen der Quantenmechanik (in German). Berlin: Springer.

J. von Neumann (1955). Mathematical Foundations of Quantum Mechanics. Princeton University Press.
^ Zurek, Wojciech Hubert (2009). "Quantum Darwinism". Nature Physics. 5 (3): 181–188. arXiv:0903.5082. Bibcode:2009NatPh...5..181Z. doi:10.1038/nphys1202. S2CID 119205282.
^ Schlosshauer, Maximilian (2005). "Decoherence, the measurement problem, and interpretations of quantum mechanics". Rev. Mod. Phys. 76 (4): 1267–1305. arXiv:quant-ph/0312059. Bibcode:2004RvMP...76.1267S. doi:10.1103/RevModPhys.76.1267. S2CID 7295619.
^ Fine, Arthur (2020). "The Role of Decoherence in Quantum Mechanics". Stanford Encyclopedia of Philosophy. Center for the Study of Language and Information, Stanford University website. Retrieved 11 April 2021.
^ Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. Phys. 43: 172–198. Translation as 'The actual content of quantum theoretical kinematics and mechanics' here

[1] Penrose, Roger (May 1996). "On Gravity's role in Quantum State Reduction". General Relativity and Gravitation. 28 (5): 581–600. doi:10.1007/BF02105068. ISSN 0001-7701.

[Grundlagen-2] J. von Neumann (1932). Mathematische Grundlagen der Quantenmechanik (in German). Berlin: Springer.

J. von Neumann (1955). Mathematical Foundations of Quantum Mechanics. Princeton University Press.

[Zurek-3] Zurek, Wojciech Hubert (2009). "Quantum Darwinism". Nature Physics. 5 (3): 181–188. arXiv:0903.5082. Bibcode:2009NatPh...5..181Z. doi:10.1038/nphys1202. S2CID 119205282.

[Schlosshauer-4] Schlosshauer, Maximilian (2005). "Decoherence, the measurement problem, and interpretations of quantum mechanics". Rev. Mod. Phys. 76 (4): 1267–1305. arXiv:quant-ph/0312059. Bibcode:2004RvMP...76.1267S. doi:10.1103/RevModPhys.76.1267. S2CID 7295619.

[Stanford1-5] Fine, Arthur (2020). "The Role of Decoherence in Quantum Mechanics". Stanford Encyclopedia of Philosophy. Center for the Study of Language and Information, Stanford University website. Retrieved 11 April 2021.

[6] Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. Phys. 43: 172–198. Translation as 'The actual content of quantum theoretical kinematics and mechanics' here

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$i\hbar {\frac {d}{dt}}\|\Psi \rangle ={\hat {H}}\|\Psi \rangle$ Schrödinger equation
Introduction Glossary History
Background Classical mechanics Old quantum theory Bra–ket notation Hamiltonian Interference
Fundamentals Complementarity Decoherence Entanglement Energy level Measurement Nonlocality Quantum number State Superposition Symmetry Tunnelling Uncertainty Wave function Collapse
Experiments Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Leggett–Garg inequality Mach–Zehnder Popper Quantum eraser Delayed-choice Schrödinger's cat Stern–Gerlach Wheeler's delayed-choice
Formulations Overview Heisenberg Interaction Matrix Phase-space Schrödinger Sum-over-histories (path integral)
Equations Dirac Klein–Gordon Pauli Rydberg Schrödinger
Interpretations Bayesian Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Local Superdeterminism Many-worlds Objective collapse Quantum logic Relational Transactional Von Neumann–Wigner
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