  In quantum mechanics students are taught to practice that eigenfunction of a
physical bound state must be continuous and vanishing asymptotically so that it
is normalizable in $x\in (-\infty, \infty)$. Here we caution that such states
may also give rise to infinite uncertainty in position $(\Delta x=\infty)$,
whereas $\Delta p$ remains finite. Such states may be called loosely bound and
spatially extended states that may be avoided by an additional condition that
the eigenfunction vanishes asymptotically faster than $|x|^{-3/2}$.
