Perform a modelling study of H atom in the planar (2D) case as described below Key reference: it is known (also from tutorial and homework) that for atoms: = , l/2 , so E = '/2 7 where <.> means \"average\". 1. Calculate in eV the total energy E of the ground-state \"at\" H atom (with electron moving only in plane) in 2D polar coordinates, for which case: = f: V(r)1/1(r)2 an dr /f01/J(r)2 2m dr Here use the same ground-state wave function known for the (usual) 3D case. In recommended here atomic units (au, including an as distance unit) for electron near proton at distance r: V(r) = 1/rr Then E(eV) = 27.212 E(au). Compare (make a specic statement, not only list the data) the obtained E value with that known for the (usual) 3D case. Conclude if such a 2D model reproduces the known (exact) 3D result. If not, specify is the H atom is more stable in 2D or 3D case 2. Modify the ground state wave function as I(r)= 6*" with a = constant. Gradually decrease a (from the initial value of 1 in part 1) in steps of 0.1 and recalculate E (as above) for each value of a until exact E is reproduced (which is supposed to happen well before a = 0 is reached). Use 1/00) with the so achieved best a to obtain: (1) for the 2D case and compare it with the value (1.5 an) for the 3D case (2) the most probable distance rmp for the 2D case (where r 1/]! 2 has maximum value) and compare it with the corresponding value (1 30) for the 3D case. Conclude whether electron is farther from the nucleus in the 2D or 3D case. Normalize l/ll( r) and plot it together with (normalized) u/(r) from part 1 in one graphr