Uncertainty Position 317E1D

1. The problem asks about the relationship between the uncertainty in momentum and the uncertainty in position. 2. According to the Heisenberg Uncertainty Principle, the uncertainties in position ($\Delta x$) and momentum ($\Delta p$) satisfy the inequality: $$\Delta x \cdot \Delta p \geq \frac{\hbar}{2}$$ where $\hbar$ is the reduced Planck's constant. 3. If the uncertainty in momentum is zero, i.e., $\Delta p = 0$, then the product $\Delta x \cdot 0 = 0$. 4. This contradicts the inequality because the right side is a positive constant $\frac{\hbar}{2}$. 5. Therefore, if $\Delta p = 0$, the uncertainty in position $\Delta x$ must be infinite to satisfy the inequality. 6. Hence, the uncertainty in position is infinite when the uncertainty in momentum is zero.