(Solved): (c) Show that the eigen-energy expression for the hydrogen atom \[ E_{n}=-\frac{\tilde{R}}{n^{2}} ...

(c) Show that the eigen-energy expression for the hydrogen atom \[ E_{n}=-\frac{\tilde{R}}{n^{2}} \] is consistent with the above Rydberg formula. Also obtain the relation between \( R_{H} \) and \( \tilde{R} \). (Note: the symbols used in class are different. You need to maintain consistency of your symbols. Simply copying the answers with the wrong symbols will be considered as incorrect.) d) What are Rydberg states for atomic systems? Illustrate how the formula is obtained.