We all understand that the position and momentum of a particle must satisfy
the Heisenberg Uncertainty Principle. But what does this mean? Is it
that _I_ can not know x & p with better precision? --- that the
infinitesimal _particle_ "knows" exactly where it is and how fast it is
going but an observer can not -- ie that the particle does indeed have an
exact locations and velocity, but the observer just can't know what it is?
OR does it mean that the particle is of finite size such that it takes up
a space of delta x?
Consider a particle in a 1 d box -- say of length L: How many locations
along L can the particle occupy? Assume any needed additional information.
Likewise, consider a 3 d box of sides L: how many places in the box can the
particle occupy?