Physics:Quantum superposition - Revision history

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	==Background==		==Background==
	~~{{Quantum mechanics\|cTopic=Fundamental concepts}}~~
	[[Biography:Paul Dirac\|Paul Dirac]] described the superposition principle as follows:		[[Biography:Paul Dirac\|Paul Dirac]] described the superposition principle as follows:

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	* {{cite book\|first1=J. A.\|last1=Wheeler\|first2=W.H.\|last2=Zurek\|year=1983\|title=Quantum Theory and Measurement\|publisher=Princeton University Press\|location=Princeton NJ}}		* {{cite book\|first1=J. A.\|last1=Wheeler\|first2=W.H.\|last2=Zurek\|year=1983\|title=Quantum Theory and Measurement\|publisher=Princeton University Press\|location=Princeton NJ}}
	{{DEFAULTSORT:Quantum Superposition}}		{{DEFAULTSORT:Quantum Superposition}}
	~~[[Category:Quantum mechanics]]~~

	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

	{{Sourceattribution\|Physics:Quantum superposition\|1}}		{{Sourceattribution\|Physics:Quantum superposition\|1}}

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	* Messiah, A. (1961). ''Quantum Mechanics'', volume 1, translated by G.M. Temmer from the French ''Mécanique Quantique'', North-Holland, Amsterdam.		* Messiah, A. (1961). ''Quantum Mechanics'', volume 1, translated by G.M. Temmer from the French ''Mécanique Quantique'', North-Holland, Amsterdam.
	* {{cite book\|first1=J. A.\|last1=Wheeler\|first2=W.H.\|last2=Zurek\|year=1983\|title=Quantum Theory and Measurement\|publisher=Princeton University Press\|location=Princeton NJ}}		* {{cite book\|first1=J. A.\|last1=Wheeler\|first2=W.H.\|last2=Zurek\|year=1983\|title=Quantum Theory and Measurement\|publisher=Princeton University Press\|location=Princeton NJ}}

	~~{{Quantum mechanics topics}}~~

	{{DEFAULTSORT:Quantum Superposition}}		{{DEFAULTSORT:Quantum Superposition}}
	[[Category:Quantum mechanics]]		[[Category:Quantum mechanics]]

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	It is natural to ask why ordinary everyday objects and events do not seem to display quantum mechanical features such as superposition. Indeed, this is sometimes regarded as "mysterious", for instance by Richard Feynman.<ref>Feynman, R. P., Leighton, R. B., Sands, M. (1965), § 1-1.</ref> In 1935, [[Biography:Erwin Schrödinger\|Erwin Schrödinger]] devised a well-known thought experiment, now known as Schrödinger's cat, which highlighted this dissonance between quantum mechanics and classical physics. One modern view is that this mystery is explained by [[Physics:Quantum decoherence\|quantum decoherence]].{{Citation needed\|date=September 2017}} A macroscopic system (such as a cat) may evolve over time into a superposition of classically distinct quantum states (such as "alive" and "dead"). The mechanism that achieves this is a subject of significant research. One mechanism suggests that the state of the cat is entangled with the state of its environment (for instance, the molecules in the atmosphere surrounding it). When averaged over the possible quantum states of the environment (a physically reasonable procedure unless the quantum state of the environment can be controlled or measured precisely), the resulting mixed quantum state for the cat is very close to a classical probabilistic state where the cat has some definite probability to be dead or alive, just as a classical observer would expect in this situation. Another proposed class of theories is that the fundamental time evolution equation is incomplete, and requires the addition of some type of fundamental Lindbladian, the reason for this addition and the form of the additional term varies from theory to theory. A popular theory is continuous spontaneous localization, where the Lindblad term is proportional to the spatial separation of the states. This too results in a quasi-classical probabilistic state.		It is natural to ask why ordinary everyday objects and events do not seem to display quantum mechanical features such as superposition. Indeed, this is sometimes regarded as "mysterious", for instance by Richard Feynman.<ref>Feynman, R. P., Leighton, R. B., Sands, M. (1965), § 1-1.</ref> In 1935, [[Biography:Erwin Schrödinger\|Erwin Schrödinger]] devised a well-known thought experiment, now known as Schrödinger's cat, which highlighted this dissonance between quantum mechanics and classical physics. One modern view is that this mystery is explained by [[Physics:Quantum decoherence\|quantum decoherence]].{{Citation needed\|date=September 2017}} A macroscopic system (such as a cat) may evolve over time into a superposition of classically distinct quantum states (such as "alive" and "dead"). The mechanism that achieves this is a subject of significant research. One mechanism suggests that the state of the cat is entangled with the state of its environment (for instance, the molecules in the atmosphere surrounding it). When averaged over the possible quantum states of the environment (a physically reasonable procedure unless the quantum state of the environment can be controlled or measured precisely), the resulting mixed quantum state for the cat is very close to a classical probabilistic state where the cat has some definite probability to be dead or alive, just as a classical observer would expect in this situation. Another proposed class of theories is that the fundamental time evolution equation is incomplete, and requires the addition of some type of fundamental Lindbladian, the reason for this addition and the form of the additional term varies from theory to theory. A popular theory is continuous spontaneous localization, where the Lindblad term is proportional to the spatial separation of the states. This too results in a quasi-classical probabilistic state.

	~~==See also==~~
	~~{{cols}}~~
	* Eigenstates
	* Mach–Zehnder interferometer
	* Penrose interpretation
	* Pure qubit state
	* Quantum computation
	* Schrödinger's cat
	* superposition principle
	* Wave packet
	~~{{colend}}~~

	== See also ==		== See also ==
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	{{Quantum mechanics topics}}		{{Quantum mechanics topics}}


	{{DEFAULTSORT:Quantum Superposition}}		{{DEFAULTSORT:Quantum Superposition}}

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	'''~~Quantum~~ superposition''' is a fundamental principle of ~~[[Physics:Quantum mechanics\|~~quantum mechanics]] that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation is a linear differential equation in time and position. More precisely, the state of a system is given by a linear combination of all the eigenfunctions of the Schrödinger equation governing that system.		'''superposition''' quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation is a linear differential equation in time and position. More precisely, the state of a system is given by a linear combination of all the eigenfunctions of the Schrödinger equation governing that system. An example is a qubit used in quantum information processing. The interference fringes in the double-slit experiment provide another example of the superposition principle. Paul Dirac described the superposition principle as follows: Anton Zeilinger, referring to the prototypical example of the double-slit experiment, has elaborated regarding the creation and destruction of quantum superposition:

	An example is a qubit used in quantum information processing. ~~A qubit state is most generally a superposition of the basis states <math>\|0 \rangle </math> and <math>\|1 \rangle </math>:~~

	~~<math>\|\Psi \rangle = c_0\|0\rangle + c_1\|1\rangle</math>~~

	Where <math>\|\Psi \rangle</math> is the [[Physics:Quantum state\|quantum state]] of the qubit and <math>\|0 \rangle</math>, <math>\|1 \rangle</math> denote particular solutions to the Schrödinger equation in Dirac notation weighted by the complex numbers <math>c_0</math> and <math>c_1</math>. Here <math>\|0 \rangle </math> corresponds to the classical 0 bit and<math>\|1 \rangle </math> to the classical 1 bit. The probabilities of measuring the system in the <math>\|0 \rangle</math> or <math>\|1 \rangle</math> state are given by <math> {\mid} c_0 {\mid}^2 </math> and <math> {\mid} c_1 {\mid}^2 </math> respectively (see the Born's rule).

	The interference fringes in the double-slit experiment provide another example of the superposition principle.
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