  In this paper the detailed investigation of one of the most interested models
in the non relativistic quantum mechanics of one massive particle i.e.,
introduced by G. Poeschl and E. Teller in 1933 is presented. This model
includes as particular cases two most popular and valuable models: the quasi
free particle in the box with impenetrable hard walls (i.e., the model with
confinement) and Bloch quantum harmonic oscillator, which is unconfined in
space; both models are frequently and effectively exploited in modern
nanotechnology e.g., in quantum dots and magnetic traps. We give the extensive
and elementary exposition of the potentials, wave functions and energetic
spectra of all these interconnected models. Moreover, the pressure operator is
defined following the lines of G. Helmann and R. Feynman which were the first
who introduced this idea in the late 30ies in quantum chemistry. By these means
the baroenergetic equation of state is obtained and analyzed for all three
models; in particular, it is shown the absence of the pressure for the Bloch
oscillator due to the infinite width of the box. The generalization of these
results on the case of nonzero temperature will be given later.
