  Following an intriguing heuristic argument of Bekenstein, many researches
have suggested during the last four decades that quantized black holes may be
characterized by discrete radiation spectra. Bekenstein and Mukhanov (BM) have
further argued that the emission spectra of quantized $(3+1)$-dimensional
Schwarzschild black holes are expected to be sharp in the sense that the
characteristic natural broadening $\delta\omega$ of the black-hole radiation
lines, as deduced from the quantum time-energy uncertainty principle, is
expected to be much smaller than the characteristic frequency spacing
$\Delta\omega=O(T_{\text{BH}}/\hbar)$ between adjacent black-hole quantum
emission lines. It is of considerable physical interest to test the general
validity of the interesting conclusion reached by BM regarding the sharpness of
the Schwarzschild black-hole quantum radiation spectra. To this end, in the
present paper we explore the physical properties of the expected radiation
spectra of quantized $(D+1)$-dimensional Schwarzschild black holes. In
particular, we analyze the functional dependence of the characteristic
dimensionless ratio $\zeta(D)\equiv\delta\omega/\Delta\omega$ on the number
$D+1$ of spacetime dimensions. Interestingly, it is proved that the
dimensionless physical parameter $\zeta(D)$, which characterizes the sharpness
of the black-hole quantum emission spectra, is an increasing function of $D$.
In particular, we prove that the quantum emission lines of $(D+1)$-dimensional
Schwarzschild black holes in the regime $D\gtrsim 10$ are characterized by the
dimensionless ratio $\zeta(D)\gtrsim1$ and are therefore effectively blended
together.
