(a) Calculate for the state (Equation 5.30). Hint: Do the integral first, using spheri...

(a) Calculate for the state (Equation 5.30). Hint: Do the integral first, using spherical coordinates, and setting the polar axis along r1, so that

The θ2 integral is easy, but be careful to take the positive root. You'll have to break the r2 integral into two pieces, one ranging from 0 to r1, the other from r1 to ∞. Answer: 5/4a.

(b) Use your result in (a) to estimate the electron interaction energy in the ground state of helium. Express your answer in electron volts, and add it to E0 (Equation 5.31) to get a corrected estimate of the ground state energy. Compare the experimental value. (Of course, we're still working with an approximate wave function, so don't expect perfect agreement).