Sometimes it is possible to solve Equation 7.10 directly, without having to expand 1 n in

Sometimes it is possible to solve Equation 7.10 directly, without having to expand Ψ¹_n in terms of the unperturbed wave functions (Equation 7.11). 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 E_ext (see Problem 7.45). 

your problem is to find the constants A, B, and C that solve Equation 7.10.
(ii) Use Equation 7.14 to determine the second-order correction to the ground state energy (the first-order correction is zero, as you found in Problem 7.45(a)).
(b) If the proton had an electric dipole moment p, the potential energy of the electron in hydrogen would be perturbed in the amount

(i) Solve Equation 7.10 for the first-order correction to the ground state wave function.
(ii) Show that the total electric dipole moment of the atom is (surprisingly) zero, to this order.
(iii) Use Equation 7.14 to determine the second-order correction to the ground state energy. What is the first-order correction?

Transcribed Image Text:

(A + Br + Cr²) e-ra Cos 0; c