Can the Hogwarts Express train be motorised? Can a Power Functions motor be fitted into the LEGO "Hogwarts Express" train? I have a spare motor and battery box and would like to fit them into this train.
I'll assume you mean the most recent Hogwards express but this applies to most trains: 

The simplest way to motorize most Lego steam engine sets that weren't made for motorization is to rebuild the coal car to sit on the train motor and contain the battery box. This typically results in a somewhat oversized coal car, but it's not ridiculously sized. If you are using the new Powered Up components, you don't need an IR sensor and you're done with just the battery box and motor. If you're using the older IR Power Functions you need to place the IR sensor somewhere: this typically involves rebuilding part of the locomotive. If you have the Power Functions train motor, but don't want to use the IR sensor, you can use the rechargeable battery box which has a built-in speed control switch. The downside is you have to catch the moving train to turn it off.

Building a powered self-contained locomotive is challenging as most steam locomotives are not wide enough to conceal a battery box, and the train motor isn't well suited to the typical spacing of the steam engine train wheels. Not to mention that its speed assumes small train wheels, so the larger wheels will spin as fast, but because of the larger diamter, the train will be faster. It's possible, but tricky, to build a steam engine where the front wheels use the train motor: I did it, but there are serious technical challenges to making it run reliably. I ended up having to switch the large wheels from a "flange, no-flange, flange" driver configuration to a "no-flange, flange, no-flange" configuration, so that the locomotive could go around corners.