A proton (charge ) moves in a uniform magnetic field ,

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

A proton (charge

q=+e

) moves in a uniform magnetic field

\vec B = B_z\hat z

B_z = 1.5\,\mathrm T

. The kinetic (gauge-covariant) momentum is

\hat{\vec\pi} = \hat{\vec p} - q\vec A

, and

[\hat\pi_x,\hat\pi_y] = i\hbar q B_z

for any choice of gauge giving this field. Evaluate the magnitude

|[\hat\pi_x,\hat\pi_y]|/\hbar

in SI units.