@@ -604,9 +604,9 @@ where $r$ is the distance between two atoms, $\epsilon$ is the depth of the pote
3. Expand $U(r)$ in a Taylor series around $r_0$ up to second order. By considering a second-order (=harmonic) potential approximation around the minimum ($r_0$), find an expression for the spring constant, $\kappa$, in terms of $\epsilon$ and $\sigma$.
4. Using the spring constant $\kappa$ you found earlier, find the ground state energy of the molecule by comparing the molecule to a quantum harmonic oscillator. What is the energy required to break the molecule apart?
??? hint
??? hint
Because the diatomic molecule is modeled as a one-body problem (in the center of mass rest frame of the molecule), the mass should be replaced by the [reduced mass](https://en.wikipedia.org/wiki/Reduced_mass).
Because the diatomic molecule is modeled as a one-body problem (in the center of mass rest frame of the molecule), the mass should be replaced by the [reduced mass](https://en.wikipedia.org/wiki/Reduced_mass).
5. What is the approximate number of phonons that can occupy this mode before the potential becomes anharmonic?
