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Heisenberg Uncertainty Principle for Position and Momentum

The uncertainty principle, also known as Heisenberg's uncertainty principle or Heisenberg's indeterminacy principle, is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, can be known.

The product of the measured momentum uncertainty and measured position uncertainty is greater than or equal to the Planck constant divided by 4\[Pi].

Formula

QuantityVariable["Δ​p", "Momentum"]*QuantityVariable["Δ​x", "Distance"] >= Quantity[1/(4*Pi), "PlanckConstant"]

symbol description physical quantity
Δ​p measured momentum uncertainty "Momentum"
Δ​x measured position uncertainty "Distance"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Heisenberg Uncertainty Principle for Position and \ Momentum"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Heisenberg Uncertainty Principle for Position and Momentum"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Heisenberg Uncertainty Principle for Position and Momentum"], \ {QuantityVariable["\[CapitalDelta]\[InvisibleSpace]x","Distance"] -> Quantity[12, "Nanometers"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1927

Publisher Information