Someone argues: “The velocity of a charged particle equals
PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · The formalism of quantum mechanics
The Structure of Quantum Mechanics, Ch Charged particles in electromagnetic fields
Problem
Someone argues: “The velocity of a charged particle equals p^/m, because p^ is the generator of translations exactly as for a free particle. By the canonical commutation relations, [p^x,p^y]=0 always, whatever fields are present, so the two velocity components commute and can in principle both be measured to arbitrary precision, magnetic field or not.” Find the error(s) in this argument, and give the correct commutator [v^x,v^y] for a particle of charge q and mass m in a uniform field B=Bz^.