Question

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

Answer:

No, according to the uncertainty relation, if $∆p=0$then $∆x$has 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

Uncertainty relation

Mathematically, the uncertainty relation can be stated as $\mathit{\Delta }\mathit{x}\mathit{\Delta }\mathit{p}\mathbf{⩾}\frac{\mathbf{h}}{\mathbf{2}}$.

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 $∆x=\infty$.

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