A3. Let us consider the hydrogen atom. In the center of the atom we have a proton and outside we have the electron. In the Bohr model, the electron is a small particle circling the proton at a certain distance from the center. In the quantum mechanical model (also called the Schrodinger model), the electron is a particle exactly then when we observe it, and otherwise it is a wave around the proton. We call that wave-function gong\". n denotes a positive integer and represents the energy level of the electron, and there are only a discrete amount of energy-levels and not a continuous amount (this is the reason we call it quantum mechanics, from the Latin word 'quant', or discrete elements of energy), 1 denotes the angular quantum momentum (or quantum level), and m = l, l + 1, . . . , l 1, l is the magnetic quantum momentum (or quantum level). The wave function ngM is different for any combination of n, l, m, and thus the electron can be the wave- function from any of those combinations. The wave-function (nahm is complex, in general. However, it is real for some combinations of n, l, m. For this problem we consider 519,003, 9,2) = 01 (p, _ e 52,o,o($,y,z) = 02 (2 08 2 a _ e Z,I,0($ayiz) = 03p [303(6) 8 2 3 where p, (p, 6 correspond to the spherical coordinates, as dened in Section 15.8. Those three functions are all real functions. The probability to nd the electron at a point (as, y, z) is given through fn,l,m(93a y, z) = |n,;,m(m, y, z)|2. (a) The probability to nd the electron somewhere in space must be one, thus fffRa fn,;,m(x, y, z)dV = 1. Use that equation to determine 01