Chapter 28, Problem 7Q

To determine

The limits set on single measurements of position by the Uncertainty Principle.

Answer to Problem 7Q

Solution:

Yes, the Uncertainty Principle sets limit on the single measurements of position. If position is accurately known, there is infinite error (no knowledge whatsoever)of velocity of that particle.

Explanation of Solution

The Heisenberg Uncertainty Principle states that simultaneous precise measurement of position and momentum is impossible, and some relative error will always be produced. Therefore, any attempt to improve measurements of position is bound to become increasing inaccurate in the determination of momentum, and thereby velocity and future trajectory.

$\begin{array}{l}△x△p\ge \frac{h}{4\pi }\\ \underset{x\to 0}{\lim }△x\to \underset{p\to \infty }{\lim }△p\end{array}$

This sets an experimental limit to the accuracy of measurement of any single quantity – position or momentum of quantum particles.