As an explicit example of the method developed in Problem 8.22, consider an electron at rest in a uniform magnetic field B = B_zk̂, for which the Hamiltonian is (Equation 4.158):

The eigenspinors, χ_a and χ_b, and the corresponding energies, E_a and E_b, are given in Equation 4.161. Now we turn on a perturbation, in the form of a uniform field in the x direction:

(a) Find the matrix elements of H', and confirm that they have the structure of Equation 8.74. What is h?
(b) Using your result in Problem 8.22(b), find the new ground state energy, in second-order perturbation theory.
(c) Using your result in Problem 8.22(c), find the variational principle bound on the ground state energy.

= eBz m -Sz. (8.76)