  Motivated by quantum mechanical corrections to the Newtonian potential, which
can be translated into an $\hbar$-correction to the $g_{00}$ component of the
Schwarzschild metric, we construct a quantum mechanically corrected metric
assuming $-g_{00}=g^{rr}$. We show how the Bekenstein black hole entropy $S$
receives its logarithmic contribution provided the quantum mechanical
corrections to the metric are negative. In this case the standard horizon at
the Schwarzschild radius $r_S$ increases by small terms proportional to $\hbar$
and a remnant of the order of Planck mass emerges. We contrast these results
with a positive correction to the metric which, apart from a corrected
Schwarzschild horizon, leads to a new purely quantum mechanical horizon.
