Larmor Clock and Friedel Sum Rule

We start this chapter by showing that spin in quantum mechanics is a very counter-intuitive entity. While a rotating classical object in a force field undergoes precession, one cannot identify spin in quantum mechanics with any physical rotation. Yet we can draw some analogies between a quantum spin in an eigen-state with physical rotation to arrive at the pivotal formalism that can allow one to theoretically study the transport and thermodynamic properties of the general mesoscopic system described with respect to Fig. 2.8 . It will lead to a hierarchy of formulas leading up to the Friedel sum rule that relates density of states to scattering phase shifts. The hierarchy members are not found in the axiomatic framework of quantum mechanics and we need the Landauer-Buttiker formalism to get them. Application of this formalism is relevant to electronic charge related effects like magnetization, polarization, AC response, non-linear response, etc., because that is where we can directly extend the Landauer philosophy.