Well, you're not wrong per se... but I believe that the Δp you have shown refers to the variance (or might say the standard deviation... the square root of the variance) of the expectation <p> (ie <p2
> - <p>2
). So, I believe the correct way to interpret this result is to say that the velocity of an object is centered around a certain value with an uncertainty given by this deviation. In that sense, the probability of measuring the velocity of a rest object at exactly zero is more probable than measuring it at any other value... but this probability is still zero.
Actually in solid state physics, people are often concerned with calculating phonon modes in low dimensional systems.
Side Bar: For those of you not in the know... a phonon mode in an array of atoms is analogous to the vibration found in a matrix of balls with each ball attached to its nearest neighbors by springs.
There is a lowest
energy value a system can have... due to your reasoning. It is refered to as the zero point energy