= Solution
Use the common $D_{3/2}$ level to subtract the two upper-state energies. The indicated transition satisfies
$$
\frac1\lambda=\frac1{397\ \mathrm{nm}}+\frac1{850\ \mathrm{nm}}-\frac1{866\ \mathrm{nm}},
\qquad
\boxed{\lambda\simeq393.6\ \mathrm{nm}.}
$$
The value inherits the rounding of the supplied <wavelengths>. It is shorter than 397 nm because $P_{3/2}$ lies above $P_{1/2}$.
A static electric potential alone cannot confine a charge stably in all three dimensions in a charge-free region. An RF quadrupole <ion trap> uses a rapidly alternating <electric field> to provide effective radial confinement; DC endcap fields can supply axial confinement. Near a stable equilibrium, the <Paul trap secular motion>[secular motion] sees an approximately harmonic pseudopotential. It has quantized vibrational levels $E=\sum_i\hbar\omega_i(n_i+1/2)$, with separate <normal modes> along the principal directions. RF <Paul trap micromotion> is superposed on this slower secular <oscillation>. For several <trapped ions>, Coulomb interactions instead give collective <normal modes>. <Nobel Lecture: Superposition, entanglement, and raising Schrödinger’s cat by David J. Wineland>[Sections III–IV, trapped-ion confinement and quantized motion]{ref}
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