  Although still under debate, observations generally suggest that dwarf
spheroidal (dSph) galaxies exhibit large constant-density cores in the centers,
which can hardly be explained by dissipationless cold dark matter simulations
without baryonic feedback. Wave dark matter (${\psi {\rm DM}}$), characterized
by a single parameter, the dark matter particle mass $m_{\psi}$, predicts a
central soliton core in every galaxy arising from quantum pressure against
gravity. Here we apply Jeans analysis assuming a soliton core profile to the
kinematic data of eight classical dSphs so as to constrain $m_{\psi}$, and
obtain $m_{\psi}=1.18_{-0.24}^{+0.28}\times10^{-22}{\,\rm eV}$ and
$m_{\psi}=1.79_{-0.33}^{+0.35}\times10^{-22}{\,\rm eV}~(2\sigma)$ using the
observational data sets of Walker et al. (2007) and Walker et al. (2009b),
respectively. We show that the estimate of $m_{\psi}$ is sensitive to the dSphs
kinematic data sets and is robust to various models of stellar density profile.
We also consider multiple stellar subpopulations in dSphs and find consistent
results. This mass range of $m_{\psi}$ is in good agreement with other
independent estimates, such as the high-redshift luminosity functions, the
reionization history, and the Thomson optical depth to the cosmic microwave
background.
