Consider the Hamiltonian of a spinless particle of charge e and mass m. In the presence of a static magnetic field, the interaction term can be generated by eA (1) рр с where is the momentum operator vector, and A is the magnetic vector potential. Suppose for р simplicity that the magnetic field is a uniform field B in the z-direction. Prove that the above prescription indeed leads to the correct expression for the interaction of the orbital magnetic moment (e/2mc)L with the magnetic field B. Show that there is an extra term proportional to B2(x 2) and comment briefly on its physical significance

Consider the Hamiltonian of a spinless particle of charge e and mass m. In the presence of a static magnetic field, the interaction term can be generated by eA (1) рр с where is the momentum operator vector, and A is the magnetic vector potential. Suppose for р simplicity that the magnetic field is a uniform field B in the z-direction. Prove that the above prescription indeed leads to the correct expression for the interaction of the orbital magnetic moment (e/2mc)L with the magnetic field B. Show that there is an extra term proportional to B2(x 2) and comment briefly on its physical significance