  Single-atomic impurities immersed in a dilute Bose gas in the spherically
symmetric harmonic trap potentials are studied at zero temperature. In order to
find the ground state of the polarons, we present a conditional variational
method with fixed expectation values of the total angular momentum operators,
$\hat{J}^2$ and $\hat{J}_z$, of the system, using a cranking
gauge-transformation for bosons to move them in the frame co-rotating with the
impurity. In the formulation, the expectation value $\langle \hat{J^2}\rangle$
is shown to be shared in impurity and bosons, but the value $\langle
\hat{J}_z\rangle$ is carried by the impurity due to the rotational symmetry. We
also analyze the ground-state properties numerically obtained in this
variational method for the system of the attractive impurity-boson interaction,
and find that excited boson distributions around the impurity overlap largely
with impurity's wave function in their quantum-number spaces and also in the
real space because of the attractive interaction employed.
