  We found exact solutions for canonical classical and quantum dynamics for
general relativity in Horwitz general covarience theory. These solutions can be
obtained by solving the generalized geodesic equation and
Schr\"{o}dinger-Stueckelberg -Horwitz-Piron (SHP) wave equation for a simple
harmonic oscilator in the background of a two dimensional dilaton black hole
spacetime metric. We proved the existence of an orthonormal basis of
eigenfunctions for generalized wave equation. This basis functions form an
orthogonanl and normalized (orthonormal) basis for an appropriate Hilbert
space. The energy spectrum has a mixed spectrum with one conserved momentum $p$
according to a quantum number $n$. To find the ground state energy we used a
variational method with appropriate boundary conditions. A set of mode
decomposed wave functions and calculated for the Stueckelberg-Schrodinger
equation on a general five dimensional blackhole spacetime in Hamilton gauge.
