## How to quantify uncertainty

$c=\lambda v$

Jeffrey Hablewitz 2I
Posts: 71
Joined: Wed Sep 30, 2020 9:33 pm

### How to quantify uncertainty

The Heisenberg uncertainty principle formula requires one to quantify the uncertainty of momentum and position. How do you find the uncertainty of an object? What units is it measured in?

Andrew Wang 1C
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### Re: How to quantify uncertainty

The uncertainty of position or momentum is like standard deviation of either the position or momentum (velocity) of an object. For example, if an object's position was $3\pm2$ m, then $\Delta x$ would be equal to 4, as the object could be anywhere from 1 m to 5 m, and 5-1=4. Once you know the uncertainty of either position or momentum, you can solve for the other using Heisenberg's uncertainty principle equation.

The units for uncertainty are the same as what the uncertainty is of, I think. So uncertainty in position would be in meters, and uncertainty in momentum would be in kg(m/s).

Please correct me if I'm wrong, and I hope this helps!

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### Re: How to quantify uncertainty

I believe that the uncertainty for momentum and position is measured in the same units as momentum and position. For example, since the units for momentum are $\frac{kg\cdot m}{s}$, the units on the uncertainty of momentum would also be $\frac{kg\cdot m}{s}$. The same is true for the position, which typically has units in meters.

You can find the uncertainty of an object through the Heinsberg Uncertainty Equation $\Delta x\Delta p\geq \frac{h}{4\pi }$, where x is position, p is momentum and h is Plank's constant. More generally, uncertainty refers to the range of values the position or momentum can take. Since we do not know exactly what the momentum of the electron is, we can say that it is around a certain number. The uncertainty tells us the maximum amount of distance (less or more) from the number the momentum could be.