In this problem, you will use the variational method to find the optimal 1s wave functio...

In this problem, you will use the variational method to find the optimal 1s wave function for the hydrogen atom starting from the trial function with as the variational parameter. You will minimize

with respect to .

a. Show that

b. Obtain the result using the standard integrals in the Math Supplement.

c. Show that using the standard integrals in the Math Supplement.

d. You now have the result . Minimize this function with respect to and obtain the optimal value of .

e. Is E(α_optimal) equal to or greater than the true energy? Why?