  The surface Hamiltonian corresponding to the surface part of a gravitational
action has $xp$ structure where $p$ is conjugate momentum of $x$. Moreover, it
leads to $TS$ on the horizon of a black hole. Here $T$ and $S$ are temperature
and entropy of the horizon. Imposing the hermiticity condition we quantize this
Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using
this we show that the entropy of the horizon is quantized. This analysis holds
for any order of Lanczos-Lovelock gravity. For general relativity, the area
spectrum is consistent with Bekenstein's observation. This provides a more
robust confirmation of this earlier result as the calculation is based on the
direct quantization of the Hamiltonian in the sense of usual quantum mechanics.

General Relativity and Quantum Cosmology;High Energy Physics - Theory;Quantum Physics