Particle-wave duality - Revision history

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	To be more specific on the wave nature of matter, a particle moving with constant velocity, \(v\), can be ascribed a corresponding (de-Broglie) wavelength, given by		To be more specific on the wave nature of matter, a particle moving with constant velocity, \(v\), can be ascribed a corresponding (de-Broglie) wavelength, given by

	<figtable id="tab:conversion">[[File:~~Table1~~.1.~~png~~\| thumb \| 600px \|<caption>Conversion table between different neutron parameters in the most commonly used units. Examples of use: \( v \, [{\rm ms}^{-1}] = 629.6 \, k \, [\)Å\(^{-1}]\) and \( (\lambda[\)Å\(])^{-1} = 0.1106 \sqrt{E {\rm [meV]}} \).</caption>]]</figtable>		<figtable id="tab:conversion">[[File:Tabel1.1.PNG\| thumb \| 600px \|<caption>Conversion table between different neutron parameters in the most commonly used units. Examples of use: \( v \, [{\rm ms}^{-1}] = 629.6 \, k \, [\)Å\(^{-1}]\) and \( (\lambda[\)Å\(])^{-1} = 0.1106 \sqrt{E {\rm [meV]}} \).</caption>]]</figtable>

	\begin{equation}\label{dummy1979310179}		\begin{equation}\label{dummy1979310179}

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	To be more specific on the wave nature of matter, a particle moving with constant velocity, \(v\), can be ascribed a corresponding (de-Broglie) wavelength, given by		To be more specific on the wave nature of matter, a particle moving with constant velocity, \(v\), can be ascribed a corresponding (de-Broglie) wavelength, given by

	<figtable id="tab:conversion">[[File:~~Tabel1~~.1.~~PNG~~\| thumb \| 600px \|<caption>Conversion table between different neutron parameters in the most commonly used units. Examples of use: \( v \, [{\rm ms}^{-1}] = 629.6 \, k \, [\)Å\(^{-1}]\) and \( (\lambda[\)Å\(])^{-1} = 0.1106 \sqrt{E {\rm [meV]}} \).</caption>]]</figtable>		<figtable id="tab:conversion">[[File:Table1.1.png\| thumb \| 600px \|<caption>Conversion table between different neutron parameters in the most commonly used units. Examples of use: \( v \, [{\rm ms}^{-1}] = 629.6 \, k \, [\)Å\(^{-1}]\) and \( (\lambda[\)Å\(])^{-1} = 0.1106 \sqrt{E {\rm [meV]}} \).</caption>]]</figtable>

	\begin{equation}\label{dummy1979310179}		\begin{equation}\label{dummy1979310179}

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ucph>Tommy at 13:45, 26 August 2019

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One of the remarkable consequences of quantum mechanics is that matter has both particle- and wave-like nature<ref name="feynman">R. P. Feynman, ''The Feynman Lectures on Physics'' (Addison Wesley Longman, 1970)</ref>. The neutron is no exception from this. In neutron scattering experiments, neutrons behave predominantly as particles when they are created in a nuclear process, as interfering waves when they are scattered, and again as particles when they are detected by another nuclear process.

To be more specific on the wave nature of matter, a particle moving with constant velocity, \(v\), can be ascribed a corresponding (de-Broglie) wavelength, given by

<figtable id="tab:conversion">[[File:Tabel1.1.PNG| thumb | 600px |<caption>Conversion table between different neutron parameters in the most commonly used units. Examples of use: \( v \, [{\rm ms}^{-1}] = 629.6 \, k \, [\)Å\(^{-1}]\) and \( (\lambda[\)Å\(])^{-1} = 0.1106 \sqrt{E {\rm [meV]}} \).</caption>]]</figtable>

\begin{equation}\label{dummy1979310179}
\lambda = \dfrac{2 \pi \hbar}{m v} .
\end{equation}

In neutron scattering, the wave nature is often referred to in terms of the neutron ''wave number'',

\begin{equation}\label{dummy1979310179321321}
k = \frac{2 \pi}{\lambda} ,
\end{equation}

or the ''wave vector'' of length \(k\) and with same direction as the velocity:

\begin{equation}\label{eq:wavenumber}
\mathbf{k} = \dfrac{m_{\rm n} \mathbf{v}}{\hbar} .
\end{equation}

By tradition, wavelengths are measured in Å (\(10^{-10} {\rm \,m}\)), and wave numbers in Å\({}^{-1}\), although some groups rather tend to use nm and nm\({}^{-1}\). The neutron velocity is always measured in SI units: m/s. For our purpose we consider the neutrons as non-relativistic, and the neutron kinetic energy is given by

\begin{equation}\label{dummy1797195180}
E = \dfrac{\hbar^2 k^2}{2 m_{\rm n}} ,
\end{equation}

which is measured in eV or meV, where \(1 {\rm eV} = 1.60218 \cdot 10^{-19} {\rm \,J}\). A useful conversion table between velocity, wave number, wavelength, energy, and temperature, is shown in <xr id="tab:conversion">Table %i</xr><ref name="squires">G. L. Squires, ''Thermal Neutron Scattering'' (Cambridge University Press, 1978)</ref>.

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