Lack of Absolute Time in Quantum Mechanics?

Quantum mechanics seems to function at two levels in terms of probability. One level is represented by classical probabilities P(x)=W*(x)W(x) and P(p)=a*(p)a(p) where W(x)=wavefunction= Sum over p a(p)exp(ipx). For a free particle this level maps into continuous space and time i.e. exp(-iEt+ipx)*exp(-iEt+ipx)=1, but at a more fundamental level (the wavefunction level) there seems to be spatial and time resolution. Spatial resolution for a free particle is based on exp(ipx) i.e. a resolution pattern cos(px) and its space shifted sin(px) representing motion. This resolution carries over to bound states for which P(x) is not 1, but is represented by crests and troughs. exp(-iEt) represents resolution in time, we argue and is linked to 1/E where E is an energy associated with an interaction. As a result a bound system may have an overall exp(-i (M1 + m2 + En) t)   where En is binding energy and an overall frequency (or spatial resolution of 1/(M1 + m2 + En), but exp(-iEnt) represents a frequency of 1/En which is linked to the interaction between M1 and m2. Thus the time resolution seems to be associated with energy and there may be various kinds of energy in a system (e.g. rest mass energy, binding energy) etc. These appear to be linked to different time resolutions. If En becomes 0, i.e. M1 and m2 no longer interact, then M1 has a time resolution proportional to 1/M1 and m2, to 1/m2. Thus at the wavefunction level it does not seem there is an absolute time, rather there are various time resolutions associated with different energies.