  Thermodynamic properties of the one-dimensional (1D) quantum well (QW) with
miscellaneous permutations of the Dirichlet (D) and Neumann (N) boundary
conditions (BCs) at its edges in the perpendicular to the surfaces electric
field $\mathscr{E}$ are calculated. For the canonical ensemble, analytical
expressions involving theta functions are found for the mean energy and heat
capacity $c_V$ for the box with no applied voltage. Pronounced maximum
accompanied by the adjacent minimum of the specific heat dependence on the
temperature $T$ for the pure Neumann QW and their absence for other BCs are
predicted and explained by the structure of the corresponding energy spectrum.
Applied field leads to the increase of the heat capacity and formation of the
new or modification of the existing extrema what is qualitatively described by
the influence of the associated electric potential. A remarkable feature of the
Fermi grand canonical ensemble is, at any BC combination in zero fields, a
salient maximum of $c_V$ observed on the $T$ axis for one particle and its
absence for any other number $N$ of corpuscles. Qualitative and quantitative
explanation of this phenomenon employs the analysis of the chemical potential
and its temperature dependence for different $N$. It is proved that critical
temperature $T_{cr}$ of the Bose-Einstein (BE) condensation increases with the
applied voltage for any number of particles and for any BC permutation except
the ND case at small intensities $\mathscr{E}$ what is explained again by the
modification by the field of the interrelated energies. It is shown that even
for the temperatures smaller than $T_{cr}$ the total dipole moment $\langle
P\rangle$ may become negative for the quite moderate $\mathscr{E}$. For either
Fermi or BE system, the influence of the electric field on the heat capacity is
shown to be suppressed with $N$ growing.
