As an explicit example of the method developed in Problem 8.22, consider an electron at rest in
Question:
As an explicit example of the method developed in Problem 8.22, consider an electron at rest in a uniform magnetic field B = Bzk̂, for which the Hamiltonian is (Equation 4.158):
The eigenspinors, χa and χb, and the corresponding energies, Ea and Eb, 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.
Step by Step Answer:
Introduction To Quantum Mechanics
ISBN: 9781107189638
3rd Edition
Authors: David J. Griffiths, Darrell F. Schroeter