The states of the electron and proton in hydrogen are entangled. Which means that the momentum and position of both are entangled. Can this be shown in an experiment, so if you measure the momentum (or a small range of them) of the proton you will know in advance what the momentum of the electron will be?  

If you first have to separate them, to do a measurement on them, will the information of the entanglement show itself in the measurement? As the information of entanglement of two spin states can show itself in measurement?