The formula to calculate the minimum uncertainty (momentum uncertainty, up) is:
\[ \text{up} = \frac{h}{4 \pi \text{ux}} \]
Where:
The minimum uncertainty, also known as momentum uncertainty, is derived from Heisenberg's Uncertainty Principle. It represents the smallest possible value for the uncertainty in momentum given a specific uncertainty in position. This principle is fundamental in quantum mechanics, highlighting the intrinsic limitations in measuring certain pairs of complementary properties simultaneously.
Let's assume the following value:
Using the formula to calculate the minimum uncertainty (up):
\[ \text{up} = \frac{h}{4 \pi \text{ux}} = \frac{6.62607015 \times 10^{-34}}{4 \pi \times 1 \times 10^{-10}} \approx 5.27 \times 10^{-25} \text{ kg·m/s} \]
The minimum uncertainty (up) is approximately \(5.27 \times 10^{-25}\) kg·m/s.
