Truthfully, it is definitely possible to get back an ex girlfriend -- even if you cheated on her.  It happens every day, and couples who have been through even worse situations than infidelity find ways to get back together.  If you really want to get her back and prove to her that you've changed, you need to follow a few rules.

First, if you want to get back your ex girlfriend after you cheated, you have to make sure that you are willing to change and never let this happen again.  You have to know deep down that you really will not cheat on her anymore, otherwise no amount of talking to her will make you believe her.

Second, you have to be willing to do the work to change the relationship.  If you cheated on your girlfriend and you want her back, you don't have to be her doormat, but you do have to be 100% trustworthy and predictable.  If you want to get her back, she will need to know where you are at all times, who you are out with, and she's probably going to want to check your phone, facebook, and email accounts.  It is perfectly normal and as long as you have nothing to hide, it shouldn't matter to you.

Third, you need to lower your expectations.  When you want to get back an ex girlfriend after you cheated on her, you need to be realistic.  If she takes you back she is not going to trust you for a very long time.  You can't get her back and then three weeks later tell her she's being unreasonable when she wants to know what you're doing after work tomorrow.  She will need a lot of time to trust you again and you can't get mad at her for needing it.