Animation of the <a href="https://en.wikipedia.org/wiki/Wave_function" class="extiw" title="en:Wave function">quantum wave function</a> of a <a href="https://en.wikipedia.org/wiki/Squeezed_state" class="extiw" title="en:Squeezed state">squeezed state</a> in a <a href="https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator" class="extiw" title="en:Quantum harmonic oscillator">Quantum harmonic oscillator</a> consisting only of the first two energy eigenstates. The <a href="https://en.wikipedia.org/wiki/Probability_distribution" class="extiw" title="en:Probability distribution">probability distribution</a> is drawn along the ordinate, while the phase is encoded by color. The best squeezing reached is a reduction in standard deviation by a factor of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {3/4}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>3</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>4</mn></msqrt></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle {\sqrt {3/4}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bad8613c69b6f9ae2860e9c18fce1abbefedb591" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:5.811ex; height:4.843ex;" alt="{\displaystyle {\sqrt {3/4}}}"></span> with the initial wavefunction
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vert \psi \rangle =\cos(\pi /6)\cdot \vert 0\rangle +\sin(\pi /6)\cdot \vert 1\rangle }"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo fence="false" stretchy="false">|</mo><mi>ψ<!-- ψ --></mi><mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo><mo>=</mo><mi>cos</mi><mo>⁡<!-- ⁡ --></mo><mo stretchy="false">(</mo><mi>π<!-- π --></mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>6</mn><mo stretchy="false">)</mo><mo>⋅<!-- ⋅ --></mo><mo fence="false" stretchy="false">|</mo><mn>0</mn><mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo><mo>+</mo><mi>sin</mi><mo>⁡<!-- ⁡ --></mo><mo stretchy="false">(</mo><mi>π<!-- π --></mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>6</mn><mo stretchy="false">)</mo><mo>⋅<!-- ⋅ --></mo><mo fence="false" stretchy="false">|</mo><mn>1</mn><mo fence="false" stretchy="false">⟩<!-- ⟩ --></mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \vert \psi \rangle =\cos(\pi /6)\cdot \vert 0\rangle +\sin(\pi /6)\cdot \vert 1\rangle }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd7617761dde4f89975f5024e732f83a31ece55b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:34.689ex; height:2.843ex;" alt="{\displaystyle \vert \psi \rangle =\cos(\pi /6)\cdot \vert 0\rangle +\sin(\pi /6)\cdot \vert 1\rangle }"></span></dd></dl>
<a href="//commons.wikimedia.org/wiki/User:Geek3" title="User:Geek3">Geek3</a>
CC BY 3.0
This  plot was created with <a href="https://en.wikipedia.org/wiki/Matplotlib" class="extiw" title="w:Matplotlib">Matplotlib</a>.