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Problem 2 On the hydrogen atom 8 (1+1+1+2+3) points Having derived the wave function for the hydrogen atom we will now have a closer look at the solution. (a) Which symmetry does the wave function for € = 0 obey? (b) Why are the wave functions for a fixed n called orbit? Which symmetry holds for the sum of those wave functions? (without proof) (c) What is the probability of finding an electron at a distance r to r+ dr from the nucleus? Sketch the radial probability density for n = 1,2. (d) There is at least one state (n.l.m) for each n. How many degenerate states are there for a fixed n? Write down the explicit states in a table for n = 1,2,3. (e) Calculate the expectation value for the distance of an electron in the ground state to the nucleus, <r>. Compare that value to the Bohr radius.