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Chapter 4: Q8CQ (page 134)

Question: When we refer to a “bound” particle, we usually mean one for which there is no probability of finding it outside some finite confines. Could a bound particle be perfectly dead stationary, meaning a well-defined velocity of zero? Why or why not?

Short Answer

Expert verified

Answer:

No, according to the uncertainty relation, if ∆p=0then ∆xhas to be infinity, however, this can’t occur with a particle in a box that has definite uncertainty in the position.

Step by step solution

01

Uncertainty relation

Mathematically, the uncertainty relation can be stated as ΔxΔp⩾h2.

02

Explanation

The uncertainty connection does not permit this, though. The positional uncertainty of a particle contained in a box is known, but since the particle is stationary means∆p=0 , the positional uncertainty is unknown indefinitely ∆x=∞.

As a result, being stationary and being enclosed in a box cannot happen at the same time.

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