On the Period Function $$T_1$$

Abstract

Associated with every effective potential, \(U_{\mathrm{eff}}(r, \ell )=U_Q(r)+\frac{\ell ^2}{2r^2}\) is a period function \(T_1(\cdot , \ell )\) that is defined for certain energies \(e\in [e_{\mathrm{min}}(\ell ), e_0]\), for which periodic solutions of \(\ddot{r}=-U'_{\mathrm{eff}}(r, \ell )\) do exist; see Appendix I, Section A.1, for more information.