Sometimes it is possible to solve Equation 6.10 directly, without having to expand in te...

Sometimes it is possible to solve Equation 6.10 directly, without having to expand in terms of the unperturbed wave functions (Equation 6.11). Here are two particularly nice examples.

(a) Stark effect in the ground state of hydrogen.

(i) Find the first-order correction to the ground state of hydrogen in the presence of a uniform external electric field (the Stark effect—see Problem 6.36)) Hint: Try a solution of the form

your problem is to find the constants A, B, and C that solve Equation 6.10.

(ii) Use Equation 6.14 to determine the second-order correction to the ground state energy the first-order correction is zero, as you found in Problem 6.36(a))) Answer:

(b) If the proton had an electric dipole moment p, the potential energy of the electron in hydrogen would be perturbed in the amount

H, ep cos 0 4re eor2

(i) Solve Equation 6.10 for the first-order correction to the ground state wave function.