Bosonic Oscillator on the de Sitter and the Anti-de Sitter Spaces

In this work, we present the exact solution of the bosonic oscillator subjected to the interaction of an uniform electric field on the de Sitter and anti de Sitter spaces. In both cases, we extract the energy spectrum and the associated wave functions. For de Sitter case, the wave functions are expressed according to the Jacobi polynomial and for anti de Sitter case, the wave functions are expressed according to Romanovski's polynomial. Finally the limiting cases are studied. (author)