In quantum mechanics, the uncertainty principle indicates that the more accurately we know a particle's position, the less accurately we can know its momentum. Which of the following statements best describes this relationship in terms of probabilities?

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Seekh · Accepted Answer

The uncertainty principle means that if a particle’s position is described by a narrow probability distribution, its momentum distribution must be broad, and vice versa. This trade‑off is expressed mathematically by the product of the standard deviations of position and momentum being at least ħ/2, so a small Δx forces a large Δp. In practical terms, if we measure the particle’s position very precisely, the probability of finding a specific momentum becomes very spread out, making momentum hard to predict. For example, a particle confined to a 1‑meter box has a very sharp position probability but its momentum probability is spread over many values, reflecting the large uncertainty in momentum.

In quantum mechanics, the uncertainty principle indicates that the more accurately we know a particle's position, the less accurately we can know its momentum. Which of the following statements best describes this relationship in terms of probabilities?

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