= Circular modes of a charged isotropic oscillator
{title2=$\omega_\pm=(-\omega_c\pm\sqrt{\omega_c^2+4\omega_0^2})/2$}
An isotropic planar <harmonic oscillator> of positive charge in a perpendicular <magnetic field> has two circular <normal modes> of opposite handedness. With $\omega_c=qB/m>0$ and $\omega_0^2=k/m$, the signed angular frequencies have the displayed form for trajectories $x+iy\propto e^{i\omega t}$. A static <electric field> shifts the equilibrium without changing these frequencies. The clockwise mode has the larger <frequency> magnitude.
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