As an undergraduate exercise, in an article (2012 Am. J. Phys. 80
[http://dx.doi.org/10.1119/1.4720101] 780–14 ), quantum and classical uncertainties for
dimensionless variables of position and momentum were evaluated in three potentials: infinite well,
bouncing ball, and harmonic oscillator. While original quantum uncertainty products depend on
##IMG## [http://ej.iop.org/images/0143-0807/37/5/055411/ejpaa3166ieqn1.gif] {${\rm{\hslash }}$} and
the number of states ( n ), a dimensionless approach makes the comparison between quantum
uncertainty and classical dispersion possible by excluding ##IMG##
[http://ej.iop.org/images/0143-0807/37/5/055411/ejpaa3166ieqn2.gif] {${\rm{\hslash }}$} . But the
question is whether the uncertainty still remains dependent on quantum number n . In the
above-mentioned article, there lies this contrast; on the one hand, the dimensionless quantum
uncertainty of the potentia…