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Chapter 34: Problem 12

If you measure a particle's position with perfect accuracy, what do you know about its momentum?

Short Answer

Expert verified
If a particle's position is measured with perfect accuracy, its momentum is completely uncertain according to Heisenberg's Uncertainty Principle.

Step by step solution

01

Understanding Heisenberg's Uncertainty Principle

Heisenberg's Uncertainty Principle asserts that both the position (x) and momentum (p) of a particle cannot be precisely measured simultaneously. The more accurately we know one of these values, the less accurately we can know the other.
02

Applying the Principle to the Given Exercise

The question states that the position of a particle is measured with 'perfect accuracy'. This means the uncertainty in position (\( \Delta x \)) is zero. As per Heisenberg's principle, if \( \Delta x = 0 \), the uncertainty in momentum (\( \Delta p \)) would be maximized. Therefore, nothing specific can be said about the momentum of the particle.
03

Conclusion Based on the Principle

Therefore, if the position of a particle is known with perfect accuracy, its momentum is completely uncertain. This is in accordance with Heisenberg's Uncertainty Principle.

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