Editing Wave function collapse (section)

===Meaning of the expansion coefficients===
The [[complex number|complex]] coefficients <math>\{c_{i}\}</math> in the expansion of a quantum state in terms of eigenstates <math>\{| \phi_i \rangle\}</math>, 
<math display=block> | \psi \rangle = \sum_i c_i | \phi_i \rangle.</math>
can be written as an (complex) overlap of the corresponding eigenstate and the quantum state:
<math display=block>  c_i  = \langle  \phi_i | \psi \rangle .</math>
They are called the [[probability amplitude]]s. The [[Absolute value#Complex numbers|square modulus]] <math>|c_{i}|^{2}</math> is the probability that a measurement of the observable yields the eigenstate <math>| \phi_i \rangle</math>. The sum of the probability over all possible outcomes must be one:<ref>{{cite book|last=Griffiths|first=David J.|title=Introduction to Quantum Mechanics, 2e|year=2005|publisher=Pearson Prentice Hall|location=Upper Saddle River, New Jersey|isbn=0131118927|pages=107}}</ref>
:<math>\langle \psi|\psi \rangle = \sum_i |c_i|^2 = 1.</math>

As examples, individual counts in a [[double slit experiment]] with electrons appear at random locations on the detector; after many counts are summed the distribution shows a wave interference pattern.<ref name="Bach Pope Liou Batelaan 2013 p=033018">{{cite journal | last1=Bach | first1=Roger | last2=Pope | first2=Damian | last3=Liou | first3=Sy-Hwang | last4=Batelaan | first4=Herman | title=Controlled double-slit electron diffraction | journal=New Journal of Physics | publisher=IOP Publishing | volume=15 | issue=3 | date=2013-03-13 | issn=1367-2630 | doi=10.1088/1367-2630/15/3/033018 | page=033018 | arxiv=1210.6243 | bibcode=2013NJPh...15c3018B | s2cid=832961 | url=https://iopscience.iop.org/article/10.1088/1367-2630/15/3/033018}}</ref> In a [[Stern-Gerlach experiment]] with silver atoms, each particle appears in one of two areas unpredictably, but the final conclusion has equal numbers of events in each area.

This statistical aspect of quantum measurements differs fundamentally from [[classical mechanics]]. In quantum mechanics the only information we have about a system is its wave function and measurements of its wave function can only give statistical information.<ref name=GriffithsSchroeter3rd/>{{rp|17}}