Editing Uncertainty principle (section)

===Coherent states===
{{Main article|Coherent state}}
A coherent state is a right eigenstate of the [[annihilation operator]],
<math display="block">\hat{a}|\alpha\rangle=\alpha|\alpha\rangle,</math>
which may be represented in terms of [[Fock state]]s as
<math display="block">|\alpha\rangle =e^{-{|\alpha|^2\over2}} \sum_{n=0}^\infty {\alpha^n \over \sqrt{n!}}|n\rangle</math>

In the picture where the coherent state is a massive particle in a quantum harmonic oscillator, the position and momentum operators may be expressed in terms of the annihilation operators in the same formulas above and used to calculate the variances,
<math display="block">\sigma_x^2 = \frac{\hbar}{2 m \omega},</math>
<math display="block">\sigma_p^2 = \frac{\hbar m \omega}{2}.</math>
Therefore, every coherent state saturates the Kennard bound
<math display="block">\sigma_x \sigma_p = \sqrt{\frac{\hbar}{2 m \omega}} \, \sqrt{\frac{\hbar m \omega}{2}} = \frac{\hbar}{2}. </math>
with position and momentum each contributing an amount <math display="inline">\sqrt{\hbar/2}</math> in a "balanced" way. Moreover, every [[squeezed coherent state]] also saturates the Kennard bound although the individual contributions of position and momentum need not be balanced in general.