  New quantum modes of the free scalar field are derived in a special
time-evolution picture that may be introduced in moving charts of de Sitter
backgrounds. The wave functions of these new modes are solutions of the
Klein-Gordon equation and energy eigenfunctions, defining the energy basis.
This completes the scalar quantum mechanics where the momentum basis is
well-known from long time. In this enlarged framework the quantization of the
scalar field can be done in canonical way obtaining the principal conserved
one-particle operators and the Green functions.
