Purpose of the Equation

[Drew Myers 4G]

So after hearing both a lecture and a discussion section about this equation, I am still incredibly confused as to what its purpose/use is. What is the purpose of this equation?

[Jada Brown 2H]

The equation is based on the idea that the exact speed of a particle and the exact position of a particle cannot be known exactly at the same time. However, this equation can be used to determine the uncertainty of one or the other, when the opposite is given.

[Amanda Lin 2I]

If the position is more precise, the momentum is more uncertain. If the momentum is more precise, the position is more uncertain. The equation calculates this uncertainty.

[Lauren Sanchez 3D]

So as the uncertainty of one variable goes up, the other goes down?

[Natalie Wang 1B]

Yes! The uncertainty of momentum and the uncertainty of position are indirectly proportional. If you change the equation, you will see that:
p >= h/(4pi *x)
You can see that p is proportional to 1/x. So if p goes up, then x needs to go down and vice versa.

[Amy Xiao 1I]

The more you know about the velocity, the less you know about the speed, and vice versa. The reason for this according to Dr. Lavelle is that the process of observing either one of those influences the other. If you set up more sensors to get accurate velocities, you will move the electron off course and change its position. If you want to have a more precise position, you have very few values to calculate a correct velocity.

[kristi le 2F]

If one property is known, the other cannot be known simultaneously. For example, if one knows the position of an electron, it is impossible to simultaneously know the momentum.

[MTanikella_1K]

This equation shows the inverse relationship of the uncertainty of momentum and position, therefore proving that it is impossible to be certain of both values at the same time. Essentially, the more precise the momentum is, the less precise position is and vice versa.

[Adelpha Chan 1B]

So after hearing both a lecture and a discussion section about this equation, I am still incredibly confused as to what its purpose/use is. What is the purpose of this equation?

The purpose of the equation is to quantify the fact that when more is known about position, less is known about speed, and vice versa. The equation quantifies the exact uncertainty of one variable in relationship to the known uncertainty of the other variable (often given in the question).

[Leila_4G]

This is very helpful! Thank you!
And this is the same equation that Dr. Lavelle talked about how the velocity does not matter as much as the mass because when things are super small the differences in velocity don't make much of a difference?
(Sorry if that was worded very poorly!)