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
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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9faf22f-10a8-4cb5-bec9-d63452f6293a%2Fd0e79461-6302-4108-9ed6-cd5dbc0c5e56%2Ffapek5h.png&w=3840&q=75)
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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