2. Modify the ground state wave function as 1(r)= e^-ar 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(r) with the so achieved best a to obtain: (1) for the 2D case and compare it with the value (1.5 a0) 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 a0) for the 3D case. Conclude whether electron is farther from the nucleus in the 2D or 3D case. Normalize 1(r) and plot it together with (normalized) (r) from part 1 in one graph.