deBroglie_wavelength

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

Calculates the de Broglie wavelength.

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.

Returns:

lambda_dB – The de Broglie wavelength in units of meters.

Return type:

Quantity

Raises:

• 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.

Warns:

~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>