An example is the Zundel cation, H2O .-H+. . . OH2, which is suspected to be a key form in which hydronium (H30+) is found in water. In this system, the potential above, V(x), represents the energy of the central proton, H+ as a function of distance from the midpoint of the two oxygen atoms. Then, the minimum on the left represents the H30+···0H2 conformation and the one on the right the H20.. OH conformation. Switching between these two conformations is a key step in the proton conduction in water, i.e., how an H+moves through water The Matlab codes provided solve for the energy levels and eigenfunctions for a particle in such a double well. While the parameters for the problem in the code are not quantitatively those for the Zundel cation, all of the basic behavior is captured. In this exercise you will examine how the barrier height and the atom mass affect the energy levels. The former is modulated by the O..O distance, which is continually fluctuating in liquid water. The former relates to the behavior of heavy water (D20) versus "normal" or protiated water (H20) Complete these two parts: 1) Calculate the energy levels for the mass as given in the code (corresponding to H+) for barrier heights varying between 0.3 and 1.0. This is changed by the E value in line 167 of potential wells.m. In particular, determine the value of the first excitation energy, ÎE = E2-E, as a function of this barrier height. This energy difference is sometimes referred to as the "tunneling splitting." Make a plot of ÎE versus the barrier height and discuss its behavior 2) Repeat the analysis in part 1 for double the mass (corresponding to D+) and discuss the differ- ences with the results you obtained above. (To change the mass, do so on line 36 in potential.wells.m by inserting a "2*")