Can I go back to my old job?
VERY unlikely. You can ask them if they'll let you come back.
No, you can't just go back to your old job. You will have to talk to your supervisor and see if they will take you back. You may have to fill out a new application or they may have backfilled your position and your job is no longer open.
Chances are they will not rehire you. You proved yourself a quitter.