  We studied multiple quantum harmonic oscillators in the Tsallis statistics of
entropic parameter $q>1$, separately applying the unnormalized $q$-expectation
value and the normalized $q$-expectation value (escort average). We obtained
the expressions of the energy and the Tsallis entropy, using the Barnes zeta
function. For the same oscillators, we obtained the expressions of the energy,
the Tsallis entropy, the average level of the oscillators, and the heat
capacity. Numerically, we calculated the energy, the Tsallis entropy, and the
heat capacity for various $N$ and $q$, using the expansion of the Barnes zeta
function with the Hurwitz zeta function, where $N$ is the number of independent
oscillators. It was shown from the requirement for the Barnes zeta function
that the quantity $N (q-1)$ is less than one. In the Tsallis statistics with
the unnormalized $q$-expectation value, the energy, the Tsallis entropy, and
the heat capacity are $N$-dependent and $q$-dependent. The $N$-dependences and
the $q$-dependences of these quantities at low temperature are different from
those at high temperature. The heat capacity is the Schottky-type. These
quantities are affected by zero point energy. In the Tsallis statistics with
the normalized $q$-expectation value, the $N$-dependences and the
$q$-dependences of the energy per oscillator and those of the heat capacity are
quite weak, when the equilibrium temperature, which is often called the
physical temperature, is adopted. The $N$-dependence and the $q$-dependence of
the Tsallis entropy are clearly seen.
