Theorem: SHO period-energy invariant T(E) * omega = 2*pi (exact for all E > 0)

Theorem (SHO period-omega product canonical): for the 1D harmonic oscillator H(q, p) = p^2/(2m) + m omega^2 q^2/2, the classical action S(E) along any periodic orbit of energy E evaluates to 2 pi E/omega (equal to 2 pi I with I = E/omega…