Relativistic de Broglie Angular Frequency by Momentum

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

The de Broglie angular frequency is proportional to the mass plus the square root of the sum of the squares of the mass and the momentum.

Formula

QuantityVariable["ω", "AngularFrequency"] == Quantity[1, "ReducedPlanckConstant"^(-1)]*(Quantity[-1, "SpeedOfLight"^2]*QuantityVariable["m", "Mass"] + Sqrt[Quantity[1, "SpeedOfLight"^4]*QuantityVariable["m", "Mass"]^2 + Quantity[1, "SpeedOfLight"^2]*QuantityVariable["p", "Momentum"]^2])

symbol	description	physical quantity
ω	angular frequency	"AngularFrequency"
m	mass	"Mass"
p	momentum	"Momentum"

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Examples

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Get the resource:

In[1]:=

$ResourceObject["Relativistic de Broglie Angular Frequency by \ Momentum"]$

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Get the formula:

In[2]:=

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Use some values:

In[3]:=

$FormulaData[ ResourceObject[ "Relativistic de Broglie Angular Frequency by Momentum"], \ {QuantityVariable["\[Omega]","AngularFrequency"] -> Quantity[1.`, ("Radians")/("Seconds")]}]$

Out[3]=

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Relativistic de Broglie Angular Frequency by Momentum

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