Vector potential uniform magnetic field

It is convenient to represent a constant and uniform magnetic field B pointing in the z direction by a vector potential... 

The external vector potential Aext(r,) = (l/2)(.Bext x rGi), for a uniform magnetic field, gives the spin-other orbit Zeeman gauge correction term... 

The vector potential A of the electromagnetic field corresponds to the uniform magnetic field H. Then... 

Let us take an example of an atom in a uniform magnetic field H. We locate the origin of the coordinate system on the nucleus, the choice being quite natural for an atom, and construct the vector potential at position r = (jr, y, z) as... 

We will now engage in a more elaborate application of Hiickel theory, which demonstrates the power of this simple model. The purpose is to determine the energy shifts of the eigenvalues when an annulene is brought into a uniform magnetic field, B. This field is independent of position and time. It can be defined as the curl (or rotation) of a vector potential A, and, in terms of a position vector r from a given... 

Retaining also the second term ik -r in the expansion of leads to a spatially non-uniform vector potential and electric field, as well as to a non-vanishing magnetic induction and to an interaction with molecules via the magnetic dipole and electric quadrupole operators. 

We assume a uniform magnetic field (B constant) with vector potential A = 2.B Xr, and no external electric field (so that Heiec = 0), and write down the corresponding forms of these terms. 

Near the origin of the coordinate system the field tends to that of a magnetic dipole in a uniform medium, and therefore for the vector potential we have ... 

In many cases the response to a uniform magnetic induction field, B, is required, when the vector potential can be written as A = X r, which automatically satisfies the Coulomb gauge condition, V.A = 0. The hamiltonian can then be reduced to the form... 

The magnetic Hamiltonians describe the interaction of electrons with the intramolecular perturbation, that is, the intrinsic magnetic dipoles m/, via the vector potential XXi A , and with an external, spatially uniform and time-independent magnetic field B = V x A ,... 

Calculations on molecules also face an additional problem in the choice of gauge origin. Over molecular dimensions, an applied magnetic field can be considered uniform and constant. In this case, the vector potential may be written as... 

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