The Heisenberg Equation of Motion
We turn to an alternative description of quantum theory, equivalent to Schrödinger’s. Rather simple reasoning led Heisenberg to an equation of motion based on the commutation relations of the operators involved. These commutation relations are uniquely linked to the corresponding uncertainty relations. From Heisenberg’s equation, we derive a compact and pictorial equation for magnetic spin precession, valid for any spin quantum number. When applied to the expectation value of the spin operator, this equation turns out to be identical to the classical precession equation of the spinning top. Additional terms that account for spin relaxation lead to the empirical Bloch equations widely used in spin resonance and in quantum optics.