# deBroglie_wavelength¶

plasmapy.formulary.quantum.deBroglie_wavelength(V: Unit("m / s"), particle) -> Unit("m")

Calculates the de Broglie wavelength.

Aliases: lambdaDB_

Parameters: V (Quantity) – Particle velocity in units convertible to meters per second. particle (str or Quantity) – Representation of the particle species (e.g., 'e', 'p', 'D+', or 'He-4 1+', or the particle mass in units convertible to kilograms. lambda_dB – The de Broglie wavelength in units of meters. Quantity TypeError – The velocity is not a Quantity and cannot be converted into a ~astropy.units.Quantity. UnitConversionError – If the velocity is not in appropriate units. RelativityError – If the magnitude of V is faster than the speed of light. ~astropy.units.UnitsWarning – If units are not provided, SI units are assumed

Notes

The de Broglie wavelength is given by

$\lambda_{dB} = \frac{h}{p} = \frac{h}{\gamma m V}$

where $$h$$ is the Planck constant, $$p$$ is the relativistic momentum of the particle, $$gamma$$ is the Lorentz factor, $$m$$ is the particle’s mass, and $$V$$ is the particle’s velocity.

Examples

>>> from astropy import units as u
>>> velocity = 1.4e7 * u.m / u.s
>>> deBroglie_wavelength(velocity, 'e')
<Quantity 5.18997095e-11 m>
>>> deBroglie_wavelength(V = 0 * u.m / u.s, particle = 'D+')
<Quantity inf m>