"Ritardo Treno" is a simple app to check the departure of your train.
Just open the app e you'll find a list of Trenitalia's stations near you.
With a tap you'll get the list of departures and the train status (delay/anticipation, position, acquiring time).
You can select your train and you'll get a auto-updated notification and a video countdown.
Time count is done with an atomic clock.

This app is available for Android and iOS device.