Problem 1 - Spherical harmonics (2! + lllf m)l m [9' = INPM 9 i Y,( 45! f 4" \"Hm?\" ,(cm) 3) Using GS 4.32. nd Yfmm. 1)) Are P?(9j and PHE') orthogonal? If not, compute the overlap between the functions. What about 333(5). o) and K5\"(6.qb)? Problem 2 - Innite spherical well a) The innite spherical well example is discussed in GS Example 4.1. For this potential, deter: mine the rst three allowed energies when E = 1. Give your answer in terms of a real number t' '12 lmes 27mg. . b) For each of these three energy levels1 make a plot of the radial dependence of the wavefuuctiun and the 9 dependence of the wavefunction. Problem 3 Hydrogen atom Calculate the probability that the electron is measured to be Within one Bohr radius of the nucleus for the n : 2 states of hydrogen. Discuss the differences between the results for the l : 0 and l : 1 states Feel free to use \"'olfraln alpha. or another tool to currlpute integrals