  We discuss Riemannian geometry of one-dimensional quantum harmonic
oscillator. Its wavefunction is a holomorphic section of the complex line
bundle $L_{\sf{v}}$ over the phase space $\mathbb{R}^2$. We show that the
energy eigenfunctions $\psi_n$ with $n\ge 1$, corresponding to the energy
levels $E_n$, are complex coordinates on orbifolds $\mathbb{R}^2/\mathbb{Z}_n$
embedded into $L_{\sf{v}}$, where $\mathbb{Z}_n$ is the cyclic group of order
$n$. In fact, $\psi_n (t,z)$ is a standing wave on $\mathbb{R}^2/\mathbb{Z}_n$,
where $z$ is a complex coordinate on the phase space
$\mathbb{R}^2\cong\mathbb{C}$. Oscillators are characterized by two quantum
charges $(q_l^{}, q_{\sf{v}})=(n,1)$, where $q_l^{}=n$ is the winding number
for the group U(1) acting on $\mathbb{R}^2/\mathbb{Z}_n$ and $q_{\sf{v}}^{}=1$
is the winding number for the U(1)-rotations on fibres of the bundle
$L_{\sf{v}}\to\mathbb{R}^2$, and $E_n=\hbar\omega(q_l^{}+\frac{1}{2}
q_{\sf{v}}).$ We also discuss "antioscillators" with opposite quantum charges
and the same positive energy.
