  A system of two charged particles in a harmonic trap with additional magnetic
field is considered. The problem is reduced to a single-particle one in
relative coordinates. The ground- and lowest excited-state energies and wave
functions are found. The ground state exhibits non-zero expectation value of
the velocity (kinetic momentum) and the probability current density does not
vanish as well. When the ground state becomes degenerate the expectation value
of velocity becomes discontinuous. The effects associated with turning on of
the magnetic field are studied by solving the appropriate time-dependent
Schr\"odinger equation. No substantial differences between abrupt
(discontinuous in time) and continuous switching on have been observed.
Evolution of a wave packet which is initially Gaussian is also investigated.
The wave packet loses its Gaussian nature and, after sufficiently large time, a
system of diffractive maxima and minima is built.
