deBroglie_wavelength

plasmapy.formulary.quantum.deBroglie_wavelength(V: Unit('m / s'), particle)

Return the de Broglie wavelength.

The de Broglie wavelength (\(λ_{dB}\)) of a particle is defined by

\[λ_{dB} = \frac{h}{p} = \frac{h}{γ m V}\]

where \(h\) is the Planck constant, \(p\) is the relativistic momentum of the particle, \(γ\) is the Lorentz factor, \(m\) is the mass of the particle, and \(V\) is the velocity of the particle.

Aliases: lambdaDB_

Parameters

• V (Quantity) – Particle velocity in units convertible to meters per second.

• particle (str, Particle, or Quantity) – An instance of Particle, or an equvalent representation (e.g., 'e', 'p', 'D+', or 'He-4 1+'), for the particle of interest, or the particle mass in units convertible to kg. If a Particle instance is given, then the particle mass is retrieved from the object.

Returns

lambda_dB – The de Broglie wavelength in units of meters.

Return type

Quantity

Raises

• TypeError – If the velocity is not a Quantity and cannot be converted into a Quantity.

• UnitConversionError – If the velocity is not in appropriate units.

• RelativityError – If the magnitude of V is larger than the speed of light.

Warns

UnitsWarning – If units are not provided, SI units are assumed.

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>