In quantum mechanics, students are taught to practice that the eigenfunction of a physical bound
state must be continuous and vanishing asymptotically so that it is normalizable in ##IMG##
[http://ej.iop.org/images/0143-0807/37/4/045404/ejpaa2747ieqn3.gif] {$xin (-infty ,infty )$} .
Here we caution that such states may also give rise to infinite uncertainty in the position ##IMG##
[http://ej.iop.org/images/0143-0807/37/4/045404/ejpaa2747ieqn4.gif] {$({rm{Delta }}x=infty )$} ,
whereas ##IMG## [http://ej.iop.org/images/0143-0807/37/4/045404/ejpaa2747ieqn5.gif] {${rm{Delta
}}p$} remains finite. Such states may be called loosely bound and spatially extended states, and may
be avoided by an additional condition that the eigenfunction vanishes asymptotically faster than
##IMG## [http://ej.iop.org/images/0143-0807/37/4/045404/ejpaa2747ieqn6.gif] {$| x{| }^{-3/2}$} .