Unfortunately that is not suitable for housing your betta, or anything really.
It would be great if you could upgrade to at least a 2.5g tank.
You'll also need a heater to keep him warm, and filter unless you want to be doing a 100% water change every other day.
Also as has been said, they don't get lonely. They do get bored though, so it helps to have some decoration and switch it around every once in a while.