  We study the effect of a constant uniform magnetic field on an electrically
charged massive particle (an electron) bound by a potential well, which is
described by means of a single attractive $\lambda\delta({\bf r})$ potential. A
transcendental equation that determines the electron energy spectrum is derived
and solved. The electron wave function in the ground (bound) state is
approximately constructed in a remarkable simple form. It is shown that there
arises the probability current in the bound state in the presence of a uniform
constant magnetic field. This (electric) current, being by the gauge invariant
quantity, must be observable and involve (and exercise influence on) the
electron scattering. The probability current density resembles a stack of
"pancake" vortices'' whose circulating "currents'' around the magnetic field
direction ($z$-axes) are mostly confined within the plane $z=0$. We also
compute the tunnelling probability of electron from the bound to free state
under a weak constant homogeneous electric field, which is parallel to the
magnetic field. The model under consideration is briefly discussed in two
spatial dimensions.
