Relativistic de Broglie Angular Frequency by Velocity

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 divided by the square root of 1 minus the square of the ratio between the velocity and the speed of light.

Formula

QuantityVariable["ω", "AngularFrequency"] == (Quantity[1, "SpeedOfLight"^2/"ReducedPlanckConstant"]*QuantityVariable["m", "Mass"])/Sqrt[1 + Quantity[-1, "SpeedOfLight"^(-2)]*QuantityVariable["v", "Speed"]^2]

symbol	description	physical quantity
ω	angular frequency	"AngularFrequency"
m	mass	"Mass"
v	velocity	"Speed"

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Get the resource:

In[1]:=

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

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Get the formula:

In[2]:=

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Use some values:

In[3]:=

$FormulaData[ ResourceObject[ "Relativistic de Broglie Angular Frequency by Velocity"], \ {QuantityVariable["m","Mass"] -> Quantity[1.`, "NeutronMass"], QuantityVariable["v","Speed"] -> Quantity[1, ("Meters")/("Seconds")]}]$

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Relativistic de Broglie Angular Frequency by Velocity

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