  We obtain the quantum Langevin equation (QLE) of a charged quantum particle
moving in a harmonic potential in the presence of a uniform external magnetic
field and linearly coupled to a quantum heat bath through momentum variables.
The bath is modeled as a collection of independent quantum harmonic
oscillators. The QLE involves a random force which does not depend on the
magnetic field, and a quantum-generalized classical Lorentz force. These
features are also present in the QLE for the case of particle-bath coupling
through coordinate variables. However, significant differences are also
observed. For example, the mean force in the QLE is characterized by a memory
function that depends explicitly on the magnetic field. The random force has a
modified form with correlation and commutator different from those in the case
of coordinate-coordinate coupling. Moreover, the coupling constants, in
addition to appearing in the random force and in the mean force, also
renormalize the inertial term and the harmonic potential term in the QLE.
