The second derivative of F(x), at the equilibrium point, can be used to estimate the natural frequency of vibration (ω) of the two protons in the hydrogen molecule ion (see Section 2.3). If the ground state energy (ћω/2) of this oscillator exceeds the binding energy of the system, it will fly apart. Show that in fact the oscillator energy is small enough that this will not happen, and estimate how many bound vibrational levels there are. Note: You’re not going to be able to obtain the position of the minimum—still less the second derivative at that point —analytically. Do it numerically, on a computer.