How Is Uncertainty in Position Determined for a Confined Proton?

[MarkusNaslund19]

Let's say a proton is confined to some diameter, d. What would be the uncertainty in the position?

In some questions they use delx as (1/2)d as the uncertainty in position. In other cases they use the entire d as the uncertainty. This is extremely confusing...

 

[christianjb]

Must be d/2

If I guess that the proton is in the middle, then the most I can be wrong by is d/2.

 

[m2003]

The uncertainty principle, also known as Heisenberg's uncertainty principle, states that it is impossible to know both the exact position and momentum of a particle simultaneously. This means that there will always be some degree of uncertainty in the measurement of a particle's position.

In the scenario described, the uncertainty in the position of the proton would depend on the specific measurement being taken. If the measurement is focused on the entire diameter, d, of the confinement, then the uncertainty would also be equal to d. However, if the measurement is focused on a smaller portion of the diameter, such as half of d, then the uncertainty would be equal to half of d, or (1/2)d.

The use of different symbols, such as delx, to represent the uncertainty in position may be a matter of convention or preference. What is important to understand is that the uncertainty principle applies to all particles, including protons, and it is a fundamental principle in quantum mechanics. Ultimately, the specific measurement being taken and the context of the question will determine the appropriate representation of uncertainty in position.