Induced magnetic field quantum mechanics

When a magnetic field is applied to a superconductor, a current is induced in the material which creates a new field opposed to the applied field such that B = 0 in the material (Meissner effect). The quantum mechanical current density j in the material is given by,... 

In spherically symmetric systems the induced diamagnetism depends primarily on the mean square radius of the valence electrons as the small contribution from the inner-shell electron core can usually be neglected 1 ). In the case of molecules with symmetry lower than cubic, the quantum mechanical treatment by Van Vleck 23> indicates that another term must be added to the Larmor-Langevin expression in order to calculate correctly diamagnetic susceptibilities. This second term arises because the electrons now suffer a resistance to precession in certain directions due to the deviations of the atomic potential from centric symmetry. The induced moment will now be dependent on the orientation of the molecule in the applied magnetic field and thus in general the diamagnetic susceptibility will not be an isotropic quantity 19-a8>. 

When an additional radio frequency field B = B o cos cot is added with B Bq, the dipoles are forced to precess synchroneously with the RF field B in the x-y-plane if co = (ol. This results in a macroscopic magnetic moment M = Nfi, which rotates with col in the x-y-plane and has a phase angle n/2 against B (Fig. 2.30c). The precession of the atoms becomes coherent through their coupling to the RF field. In the quantum-mechanical description, the RF field induces transitions between the Zeeman sublevels (Fig. 2.30d). If the RF field B is sufficiently intense, the atoms are in a coherent superposition of the wave functions of both Zeeman levels. 

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