Essential University Physics (3rd Edition)
Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 35, Problem 1FTD
To determine

Why a particle confined to a finite region cannot have zero energy.

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Explanation of Solution

If the ground state-state energy of a particle that confined to a finite region is zero, then it will violate the uncertainty principle. Because of the zero kinetic energy, the particle has zero momentum and then its position is absolutely determined.

That means the uncertainty in position is equal to the width of the potential well (region), then the uncertainty relation becomes ΔpΔx=0 . The statistical nature of the quantum mechanics is lost and the uncertainty principle ΔpΔx

Therefore, the particle confined to a finite region cannot have zero energy.

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