  The problem of the quantum modes of the scalar free field on anti-de Sitter
backgrounds with an arbitrary number of space dimensions is considered. It is
shown that this problem can be solved by using the same quantum numbers as
those of the nonrelativistic oscillator and two parameters which give the
energy quanta and respectively the ground state energy. This last one is known
to be just the conformal dimension of the boundary field theory of the AdS/CFT
conjecture.
