Editing Matter wave (section)

=== Special relativity ===
Using two formulas from [[special relativity]], one for the relativistic mass energy and one for the [[Momentum#Relativistic|relativistic momentum]]
<math display="block">\begin{align}
E &= m c^2 = \gamma m_0 c^2 \\[1ex]
\mathbf{p} &= m\mathbf{v} = \gamma m_0 \mathbf{v}
\end{align} </math>
allows the equations for de Broglie wavelength and frequency to be written as
<math display="block">\begin{align}
&\lambda =\,\, \frac {h}{\gamma m_0v}\, =\, \frac {h}{m_0v}\,\,\, \sqrt{1 - \frac{v^2}{c^2}} \\[2.38ex]
& f = \frac{\gamma\,m_0 c^2}{h} = \frac {m_0 c^2}{h\sqrt{1 - \frac{v^2}{c^2}}} ,
\end{align}</math>
where <math>v=|\mathbf{v}|</math> is the [[velocity]], <math>\gamma</math> the [[Lorentz factor]], and <math>c</math> the [[speed of light]] in vacuum.<ref>{{cite book |title=Stationary states |first=Alan |last=Holden |publisher=Oxford University Press |date=1971 |location=New York |isbn=978-0-19-501497-6 }}</ref><ref>Williams, W.S.C. (2002). ''Introducing Special Relativity'', Taylor & Francis, London, {{ISBN|0-415-27761-2}}, p. 192.</ref> This shows that as the velocity of a particle approaches zero (rest) the de Broglie wavelength approaches infinity.