Please use matlab to solve the problem

1. Consider an atom with its electron energy function, , as follows: 2 1 h 020 ev = Ev 2 m 4 TIe where h, m, a, and Eare reduced Planck constant, electron mass, and vacuum permittivity and total energy of electrons. (a) Please use spherical coordinate system to re-write the above equation. (b) Please use the method of separation of variables to write down the corresponding equations where you can assume the wave function is listed as follows: w..) = R(p) yle.d = R(r) @10)(6) Noted that you will have your own assumption to constitute the three independent equations. (c) Now from boundary condition in the azimuthal angle part, you can derive the first set of eigenvalues, which are called magnetic quantum numbers to let dot 27. = (@). Thus, you can further find the correlated eigenvalue sets including orbital quantum numbers, I, and principle quantum number, n Please write down the correlation between these quantum numbers. (d) Now please derive the ground state electron energy E, based on the boundary condition of R(p>0, r-* and write down the corresponding energy function, y. (e) Please derive the energy function and plot Wnim(r.0.o ) where n, l. and m are the remainder of your last three student ID numbers individually divided by 2 and then plus 3, 1, 0, respectively. (For instance, if your last three ID number is 456 then the wave function you need to derive is 0320)