Abstract
In the previous chapter, we showed how to calculate the magnetic moment of an atom. We saw that the problem is already quite involved even for a single atom if we go beyond a hydrogen-like one.
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Notes
- 1.
As we saw in the last chapter, all atoms present a diamagnetic behavior, but since it is very weak compared to the paramagnetic response, only atoms with closed shells (e.g., noble gases) present an overall diamagnetic response. An exception is of course superconducting materials, which can have a perfect diamagnetic response. This is, however, a collective, macroscopic response due to the superconducting currents which oppose the change in magnetic flux.
- 2.
Note that in general the variational procedure would be to write \(\psi _{s/t}(\mathbf {r}_{1},\mathbf {r}_{2})=c_{1}\phi _{a}(\mathbf {r}_{1})\phi _{b}(\mathbf {r}_{2})\pm c_{2}\phi _{b}(\mathbf {r}_{1})\phi _{a}(\mathbf {r}_{2})\) and find the coefficients \(c_{1,2}\) by minimizing Eq. 3.3.2. One then finds \(c_{1}=c_{2}=1/\sqrt{2}\). In Eq. 3.3.1 we used our knowledge of the symmetry of the problem plus the normalization of the wavefunctions \(\phi _{a, b}\) to write the result immediately.
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Viola Kusminskiy, S. (2019). Magnetism in Solids. In: Quantum Magnetism, Spin Waves, and Optical Cavities. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-13345-0_3
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DOI: https://doi.org/10.1007/978-3-030-13345-0_3
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