  In this work, thermal and magnetic properties for an electron with
cylindrical confinement in presence of external electric and magnetic fields
have been investigated. We found that the corresponding time-independent
Schr\"odinger equation can be separated into the product of the radially
symmetric and an axial equation. Moreover, we have obtained a quasi-exact
expression for the energy spectrum of the system in terms of the exact
solutions for the radial equation and an approximation up to first order for
the axial equation. We have calculated the well-known thermal and magnetic
properties as the heat capacity, magnetization and the magnetic susceptibility
via the canonical partition function. We found that our results for thermal and
magnetic properties differ significantly from results previously obtained by
others authors (by Gumber et. al.). Moreover, our results are in agreement with
the diamagnetic properties of GaAs.
