2. [7] Consider three particles of mass mi, m, and m (they could for example be a collection of nuclei and electrons). These particles can move in three-dimensions. The particles are charged and therefore interact with one another via a Coulombic interaction. For a given pair of particles, the potential energy of this interaction is given by: 4.7) = ZiZ 4) where Z is the charge of each particle, n, is the particle's position vector (Xi, yi, Zi) and the subscript specifies the particle in this case we have particles 1, 2 & 3). ny is the distance between the two particles. Write down the Hamiltonian operator for this system in Cartesian coordinates. HINTS: Be explicit about what particle you are referring to for each variable. . You should have no r vectors in your answer. You need to define the distance in Cartesian coordinates. Don't solve the Schrdinger equation, just write down the Hamiltonian operator. Consider the Coulomb interaction between particle pairs carefully