The Uncertainty Relation for Position and Momentum

[knowLittle]

Homework Statement

The position of a 60-gram golf ball sitting on a tee is
determined within +- 1μm. What is its minimum possi-
ble energy? Moving at the speed corresponding to this
kinetic energy, how far would the ball move in a year?

Homework Equations

## K\geq\dfrac {\hbar ^{2}} {2ma^{2}} ## Minimum Possible Kinetic E.

The Attempt at a Solution

I have solved it using the above equation. But, I wonder, if I should consider rest energy as well.

When they ask the second question, I sort of think that they only want this minimum kinetic E.
Any ideas?

Danke.

 

[mfb]

Just the kinetic energy is interesting here.

 

[knowLittle]

Why?

 

[mfb]

You can calculate both if you like, but the rest energy cannot be accessed here (as you do not have an anti-golfball), and you are not dealing with relativistic velocities.

 

[paranormal]

I would respond by saying that the Uncertainty Relation for Position and Momentum, also known as the Heisenberg Uncertainty Principle, states that it is impossible to know the exact values of both the position and momentum of a particle at the same time. This is due to the inherent limitations of measurement in quantum mechanics.

In this specific scenario, the position of the golf ball is known within +- 1μm, but this does not mean that its momentum can be known with absolute certainty. The minimum possible energy of the golf ball can be calculated using the given equation, but it is important to note that this is the minimum kinetic energy and does not account for other forms of energy such as rest energy.

As for the second question, it is unclear what the intention of the question is. It could be asking for the minimum distance the ball would move in a year based on its minimum kinetic energy, or it could be asking for the maximum distance it could potentially move due to the uncertainty in its momentum. Without further clarification, it is difficult to provide a definitive answer.