Formula: Heisenberg's Uncertainty Relation Location uncertainty Pulse uncertainty Planck's Constant
$$\Delta x \, \Delta p ~\geq~ \frac{h}{4\pi}$$
$$\Delta x ~\geq~ \frac{h}{4\pi} \frac{1}{ \Delta p }$$
$$\Delta p ~\geq~ \frac{h}{4\pi} \frac{1}{ \Delta x }$$
Location uncertainty
$$ \Delta x $$ Unit $$ \mathrm{m} $$
The position \(x\) of a particle is in the range between \(x-\Delta x\) and \(x+\Delta x\) because of the measurement uncertainty.
Pulse uncertainty
$$ \Delta p $$ Unit $$ \frac{\mathrm{kg} \, \mathrm{m}}{\mathrm{s}} $$
According to the uncertainty relation, the momentum \(p\) of the particle must have at least the deviation \(\Delta p\) which is given in principle by \(\Delta x\) and the Planck's constant \(h\). The momentum of the particle lies in the interval between \(p-\Delta p\) and \(p+\Delta p\) and this interval cannot be decreased.
Planck's Constant
$$ h $$ Unit $$ \mathrm{Js} = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{s} } $$
Planck's is a physical constant (of quantum mechanics) and has the value: \( h ~=~ 6.626 \cdot 10^{-34} \, \text{Js} \).