Gravitational D-dimensional model with l scalar fields and several forms is
considered. When cosmological type diagonal metric is chosen, an
electromagnetic composite brane ansatz is adopted and certain restrictions on
the branes are imposed the conformally covariant Wheeler-DeWitt (WDW) equation
for the model is studied. Under certain restrictions asymptotic solutions to
WDW equation are found in the limit of the formation of the billiard walls
which reduce the problem to the so-called quantum billiard on the (D+ l
-2)-dimensional Lobachevsky space. Two examples of quantum billiards are
considered. The first one deals with 9-dimensional quantum billiard for D = 11
model with 330 four-forms which mimic space-like M2- and M5-branes of D=11
supergravity. The second one deals with the 9-dimensional quantum billiard for
D =10 gravitational model with one scalar field, 210 four-forms and 120
three-forms which mimic space-like D2-, D4-, FS1- and NS5-branes in D = 10 II A
supergravity. It is shown that in both examples wave functions vanish in the
limit of the formation of the billiard walls (i.e. we get a quantum resolution
of the singularity for 11D model) but magnetic branes could not be neglected in
calculations of quantum asymptotic solutions while they are irrelevant for
classical oscillating behaviour when all 120 electric branes are present.Comment: 30 pages, Latex, no figures. Typos are eliminated; new references are
added. To be published in Eur. Phys. J.
