Talìa lu còdici di Cullassu dâ funzioni d'onda

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'Nta [[miccanica quantistica]], lu '''cullassu dâ funzioni d'onda'''  eni lu prucessu cô quali na [[funzioni d'onda]], inizziarmenti nta na [[supirpusizziona quantistica|supirpusizziona]] o autri ''[[eigenstate]]'', appari riducirsi a nu singulu statu di chiddi ca aisistinu duoppu n'intirazzioni cu n'ussirvatori.<br>
Eni unu di li dui prucessi cu li quali li [[sistema quantisticu|sistema quantistici]] ivolvunu 'nta lu tiempu sicuennu li lieggi da miccanica quantistica comu fuorru prisintati di [[John von Neumann]].<br>
A [[rialitati]] di lu cullassu di la funzioni d'onda anu a statu discurruta e si cuntinuanu a discurru macari oggi, zoè, si eni nu [[finominu]] fisicu fundamintali cu tutti li santi crisma o sulu n'[[epifinominu]] di n'autru prucessu comu putissi ssiri a [['ncuirenza quantistica]].<br>
'Nta l'urtima dicenni a 'ncuirenza quantistica avi cunquistatu pupularitati zoè si [[falsicabbilitati|falsificau]] difficirmenti.<br>

== Tirminoluggìa matimatica ==

Lu statu, o a funzioni d'onda, di nu sistema fisicu a nu certu tiempu ppo ssiri spressu nta [[nutazzioni bra-ket]] o Dirac comu:
:<math> |\psi \rang = \sum_i |i\rang \psi_i</math>
unni <math>\scriptstyle |i \rang</math> spicifica a li "altirnativi" quantichi dispunibbila (ticnicamenti, formanu na  basi [[ortonurmale]] ppi lu vitturi eigen, ca imprica <math>\scriptstyle \lang i | j \rang = \delta_{ij}</math>).  <br>
Nu paramitru ussirvabbili o misurabbili di lu sistema assuciatu cu ogni basi eigen, cu ogni altirnativa quantistica avi nu spicificu valuri o [[eigenvalue]], ''e''<sub>''i''</sub>, di l'ussirvabbili.
<!-- traduzzioni in corsu
The <math>\scriptstyle \psi_i = \lang i|\psi \rang</math> are the [[probability amplitude]] coefficients, which are [[complex numbers]].  For simplicity we shall assume that our wave function is normalised: <math>\scriptstyle \lang \psi | \psi \rang</math>, which implies that
:<math>\lang \psi|\psi \rang = \sum_i |\psi_i|^2 = 1.</math>

With these definitions it is easy to describe the process of collapse: when an external agency measures the observable associated with the eigenbasis then the state of the wave function changes from <math>\scriptstyle |\psi\rang</math> to just ''one'' of the <math>\scriptstyle |i\rang</math>s with [[Born probability]] <math>\scriptstyle | \psi_i | ^ 2</math>.  This is called collapse because all the other terms in the expansion of the wave function have vanished or collapsed into nothing. If a more general measurement is made to detect if the system is in a state <math>\scriptstyle | \phi \rang</math> then the system makes a "jump" or [[quantum leap]] from the original state <math>\scriptstyle | \psi \rang</math>  to the final state <math>\scriptstyle | \phi \rang</math>  with probability of <math>\scriptstyle |\lang \psi | \phi \rang|^2</math>.  Quantum leaps and wave function collapse are therefore opposite sides of the same coin.

==History and context==

By the time [[John von Neumann]] wrote his treatise ''Mathematische Grundlagen der Quantenmechanik'' in 1932,<ref>The "collapse" or "reduction" of the wave function was introduced by Heisenberg in his uncertainty paper and later postulated by von Neumann as a dynamical process independent of the Schrodinger equation. [http://arxiv.org/abs/quant-ph/0210152 Kiefer, C. ''On the interpretation of quantum theory – from Copenhagen to the present day'']</ref> the phenomenon of "wave function collapse" was accommodated into the [[mathematical formulation of quantum mechanics]] by postulating that there were two processes of wave function change:

# The [[probability|probabilistic]], non-[[unitary transformation|unitary]], [[local realism|non-local]], discontinuous change brought about by observation and [[quantum measurement|measurement]], as outlined above.
# The [[deterministic]], [[unitary transformation|unitary]],  continuous [[time evolution]] of an isolated system that obeys [[Schrödinger's equation]] (or nowadays some relativistic, [[local realism|local]] equivalent).

In general, quantum systems exist in [[quantum superposition|superposition]]s of those basis states that most closely correspond to classical descriptions, and -- when not being measured or observed, evolve according to the time dependent [[Schrödinger equation]], [[relativistic quantum field theory]] or some form of [[quantum gravity]] or [[string theory]], which is process (2) mentioned above.  However, when the wave function collapses -- process (1) -- from an observer's perspective the state seems to "leap" or "jump" to just one of the basis states and uniquely acquire the value of the property being measured, <math>e_i</math>, that is associated with that particular basis state. After the collapse, the system begins to evolve again according to the Schrödinger equation or some equivalent wave equation.

By explicitly dealing with the [[Measurement in quantum mechanics#Wavefunction collapse|interaction of object and measuring instrument]] von Neumann<sup>[1]</sup> has attempted to prove consistency of the two processes (1) and (2) of wave function change. 

He was able to prove the ''possibility'' of a quantum mechanical measurement scheme consistent with wave function collapse. However, he did not prove ''necessity'' of such a collapse.
Although von Neumann's projection postulate is often presented as a normative description of quantum measurement it should be realized that it was conceived by taking into account experimental evidence available during the 1930s (in particular the [[Mathematical formulation of quantum mechanics#The problem of measurement|Compton-Simon experiment]] has been paradigmatic), and that many important [[Measurement in quantum mechanics#Wavefunction collapse|present-day measurement procedures]] do not satisfy it (socalled measurements of the second kind).{{Fact|date=December 2008}}

The existence of the [[wave function]] collapse is required in

* the [[Copenhagen interpretation]] 
* the [[objective collapse interpretation]]s 
* the so-called [[transactional interpretation]]
* in a "spiritual interpretation" in which [[consciousness causes collapse]].

On the other hand, the collapse is considered as redundant or just an optional approximation in

* interpretations based on [[consistent histories]]
* the [[many-worlds interpretation]]
* the [[Bohm interpretation]]
* the [[Ensemble Interpretation]]

The cluster of phenomena described by the expression ''wave function collapse'' is a fundamental problem in the interpretation of quantum mechanics known as the [[measurement problem]]. The problem is not really confronted by the [[Copenhagen interpretation]] which simply postulates that this is a special characteristic of the "measurement" process.   The [[Everett many-worlds interpretation]] deals with it by discarding the collapse-process, thus reformulating the relation between measurement apparatus and system in such a way that the linear laws of quantum mechanics are universally valid, that is, the only process according to which a quantum system evolves is governed by the Schrödinger equation or some [[theory of relativity|relativistic]] equivalent.  Often tied in with the many-worlds interpretation, but not limited to it, is the physical process of [[decoherence]], which causes an ''apparent'' collapse. Decoherence is also important for the interpretation based on [[Consistent Histories]].

Note that a general description of the evolution of quantum mechanical systems is possible by using [[density matrix|density operators]] and [[quantum operation]]s.  In this formalism (which is closely related to the C*-algebraic formalism) the collapse of the wave function corresponds to a non-unitary quantum operation.

Note also that the physical significance ascribed to the wave function varies from interpretation to interpretation, and even within an interpretation, such as the [[Copenhagen Interpretation]].  If the wave function merely encodes an observer's knowledge of the universe then the wave function collapse corresponds to the receipt of new information -- this is somewhat analogous to the situation in classical physics, except that the classical "wave function" does not necessarily obey a wave equation.  If the wave function is physically real, in some sense and to some extent, then the collapse of the wave function is also seen as a real process, to the same extent.  One of the paradoxes of quantum theory is that wave function seems to be more than just information (otherwise interference effects are hard to explain) and often less than real, since the collapse seems to take place faster-than-light and triggered by observers.

==Notes==
<references/>

==See also==
*[[Arrow of time]]
*[[Interpretation of quantum mechanics]]
*[[Quantum decoherence]]
*[[Quantum interference]]
*[[Schrödinger's cat]]
*[[Zeno effect]]

[[Catigurìa:Quantum measurement]]
[[Catigurìa:Fundamental physics concepts]]
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