  We theoretically consider effectively one-dimensional quantum droplets in a
symmetric Bose-Bose mixture confined in a parabolic trap. We systematically
investigate ground and excited families of localized trapped modes which
bifurcate from eigenstates of the quantum harmonic oscillator as the number of
particles departs from zero. Families of nonlinear modes have nonmonotonous
behavior of chemical potential on the number of particles and feature
bistability regions. Excited states are unstable close to the linear limit, but
become stable when the number of particles is large enough. In the limit of
large density, we derive a modified Thomas-Fermi distribution. Smoothly
decreasing the trapping strength down to zero, one can dynamically transform
the ground state solution to the solitonlike quantum droplet, while excited
trapped states break in several moving quantum droplets.
