Particle Wavelengths¶

The idea of particles having wavelengths is pretty central to a lot of modern physics, and (Krane, 1988) is a good reference for the idea, but I would assume that most physics textbooks have this to come degree.

De Broglie hypothesized that every particle is also a wave (and the converse), and that we could assign them a wavelength depending on their rest mass and kinetic energy.

Mass Bearing¶

For mass bearing particles, the pythagorean distance of between the particle’s kinetic energy and rest mass energy is the total energy. Thus, we can solve the equation

\[E = \frac{hc}{\lambda}\]

with \(h = 4.135\times 10^{-5}\unit{eV\cdot s}\) as

\[\lambda = \frac{hc}{\sqrt{E_{total}^{2} - E_{rest}^{2}}}\]

Non Mass Bearing¶

For non mass bearing particles (photons), the rest mass energy is non sensical, so we get the simple result that

\[\lambda=\frac{hc}{E}\]

Particle Wavelengths¶

Mass Bearing¶

Non Mass Bearing¶

Bibliography