  The soft and hard edge scaling limits of $\beta$-ensembles can be
characterized as the spectra of certain random Sturm-Liouville operators. It
has been shown that by tuning the parameter of the hard edge process one can
obtain the soft edge process as a scaling limit. We prove that this limit can
be realized on the level of the corresponding random operators. More precisely,
the random operators can be coupled in a way so that the scaled versions of the
hard edge operators converge to the soft edge operator a.s. in the norm
resolvent sense.
