Larmor Diamagnetism Quantum Approach

Quantum mechanics does not allow the orbital angular momentum to line up with the magnetic field as assumed in the previous example. Instead L projects a component, lime on the B-direction as was shown in Chapter 2. A magnetic field exerts a torque on a magnetic moment according to L = p,M x B. This torque is perpendicular both to the field B and the L, which is along the p.b therefore, the effect is to cause a precession of L about B. This precession is knovm as Larmor precession and takes place with the Larmor frequency 

This precession represents a shell of charge rotating about the B-direction. The resulting magnetic moment is 

The effect is small, but all atoms have a small amount of diamagnetism. This includes atoms in gases and liquids, atoms in van der Waals bonded ciystals, ions in ionic salts, ion cores in metals, inner core electrons in covalently bonded crystals, and in molecules of living systems. 

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