plasmapy.formulary.quantum.deBroglie_wavelength(V: Quantity, particle: str | Integral | Particle | CustomParticle | Quantity) Quantity[source]

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_

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

  • particle (str, Particle, or Quantity) – An instance of Particle, or an equivalent 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.


lambda_dB – The de Broglie wavelength in units of meters.

Return type:



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


>>> import astropy.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>