Editing Free particle (section)

===Measurement and calculations===
The normalization condition for the wave function states that if a wavefunction belongs to the [[quantum state space]]{{sfn|Blanchard|Brüning|2015|p=210}} 
<math display="block">\psi \in L^2(\mathbb{R}^3),</math>
then the integral of the [[probability density function]]
<math display="block"> \rho(\mathbf{r},t) = \psi^*(\mathbf{r},t)\psi(\mathbf{r},t) = |\psi(\mathbf{r},t)|^2,</math>

where * denotes [[complex conjugate]], over all space is the probability of finding the particle in all space, which must be unity if the particle exists:
<math display="block"> \int_{\mathbb{R}^3} |\psi(\mathbf{r},t)|^2 d^3 \mathbf{r}=1.</math>
The state of a free particle given by plane wave solutions is ''not'' normalizable as
<math display="block">Ae^{i(\mathbf{k}\cdot\mathbf{r}-\omega t)} \notin L^{2}(\mathbb{R}^3),</math>
for any fixed time <math>t</math>. Using [[wave packet]]s, however, the states can be expressed as functions that ''are'' normalizable.

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{{multiple image
 | align = center
 | direction = horizontal
 | footer    = Interpretation of wave function for one spin-0 particle in one dimension. The wavefunctions shown are continuous, finite, single-valued and normalized. The colour opacity (%) of the particles corresponds to the probability density (which can measure in %) of finding the particle at the points on the x-axis.
 | image1    = Quantum mechanics travelling wavefunctions.svg
 | caption1  = Increasing amounts of wavepacket localization, meaning the particle becomes more localized.
 | width1    = 400
 | image2    = Perfect localization.svg
 | caption2  = In the limit ''ħ'' → 0, the particle's position and momentum become known exactly.
 | width2    = 200
}}
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