Hi,
In the above link, on page 37, there is a figure of a potential energy function of a harmonic oscillator (say a particle), specifically figure 23.22. In the figure there is also an indication of the total energy E. Is it possible for a particle to exist at the unstable maxima where the potential energy is greater than the total energy? The kinetic energy would have to be negative, which is impossible. Yet, isn’t the unstable maxima also a point of equilibrium?