An example of how one can apply quantum theory to the most mundane of things, travelling via public transport, in this case a bus.
Most buses have several rows of four seats, split down the middle; with two seats either side of the aisle. Have you noticed how when you get on a bus, the passengers already on the bus will have filled up the seats, one passenger per double-seat, up the length of the bus. Indeed, when choosing your seat, if there's an empty double-seat, you generally sit there, rather than sit next to an existing passenger. Sound familiar? It's my hypothesis that bus passengers are fermions - they hate sharing the same state, and will fill up all available energy levels (well, double-seats in this case!) before grudgingly sharing an energy level with another fermion.
Conversely, when waiting for a bus to turn up, one usually waits for some time and then finds several buses turn up at once! This also has a quantum analog; buses must be bosons - they, wherever possible, strive to stay together in the same state.
Quite what Werner Heisenberg would say about this, I don't know, but it's something to ponder at the bus stop.