Quantum and classical dissipation of charged particles

•Hamiltonian of a damped charged particle in time dependent electromagnetic fields.•Exact Green’s function of a charged particle in time dependent electromagnetic fields.•Time evolution of a Gaussian wave packet of a damped charged particle.•Classical and quantum dynamics of a damped electric charge.

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail.