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

Question

It's a quantum mechanics problem.

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
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Transcribed Image Text

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

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