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| Louis de Broglie, 1892—1987. |
Consider some particle P characterized by its wavevector $\overline{ \kappa }$ and the total number of quarks it contains $N$. Report on any changes relative to a frame of reference F which is characterized using the average wavevector$\ \ \tilde{ \kappa }$ of the quarks in F. The momentum of P in the F-frame is defined as
$\begin{align} \overline{p} \equiv \frac{h}{2\pi} \left( \overline{ \kappa }^{ \sf{P}} \! - N^{ \sf{P}} \, \tilde{ \kappa }^{ \sf{F}} \right) \end{align}$
But in a perfectly inertial frame of reference
$\tilde{ \kappa } ^{ \sf{F}}= \left( 0, 0, 0 \right)$
then the momentum of P is
$\begin{align} \overline{p} = \frac{h}{2\pi} \overline{ \kappa } \end{align}$
Recall that for particles in motion the wavelength is given by $\lambda = 2 \pi / \kappa$. So taking the norm of the momentum and eliminating the wavenumber obtains Louis de Broglie's
statement about the relationship between momentum and wavelength
$\begin{align} \lambda = \frac{ h }{ p } \end{align}$
DeBroglie's postulate notes a conditional proportionality between $\overline{p}$ and $\overline{ \kappa }$ that is simply built into the definitions used by WikiMechanics.
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De Broglie's Postulate |
