Relativistic de Broglie Wavelength by Velocity

The de Broglie wavelength is the wavelength associated with a massive particle in motion according to quantum mechanics, accounting for relativistic effects.

The de Broglie wavelength is proportional to the square root of the difference between 1 and the square of the ratio between the velocity and the speed of light. This is then divided by the mass times velocity.

Formula

QuantityVariable["λ", "Wavelength"] == (Quantity[1, "PlanckConstant"]*Sqrt[1 + Quantity[-1, "SpeedOfLight"^(-2)]*QuantityVariable["v", "Speed"]^2])/(QuantityVariable["m", "Mass"]*QuantityVariable["v", "Speed"])

symbol	description	physical quantity
λ	wavelength	"Wavelength"
m	mass	"Mass"
v	velocity	"Speed"

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$FormulaData[ ResourceObject[ "Relativistic de Broglie Wavelength by Velocity"], \ {QuantityVariable["\[Lambda]","Wavelength"] -> Quantity[400, "Nanometers"]}]$

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Relativistic de Broglie Wavelength by Velocity

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