Can you really still be friends with an ex?

NO JUDGEMENT please! I did something today that was INCREDIBLY hard to do. I broke up with my girlfriend of almost a year. Why? Because I'm married and it's wrong. I know what I've done is horrible and I'm not that kind of guy. I never meant to fall in love with somebody else. It just happened. I did not have sex with my girlfriend in the year we've been together, but we did kiss and spend a lot of time sharing with one another. We almost had sex a few times, but neither one of us could go through with it. So, after months of knowing that this had to stop we finally amicably split today. She cried and I cried, but we both agreed we couldn't keep this up. She's my best friend and what makes it worse is that I know she has nobody to take care of her. She's not super close with her parents, she's an only child, and she's not lived in our area for very long so her friend/acquaintance list is very short. I honestly cannot stand the thought of her not being my friend. Is it possible that we can salvage our friendship and still be in each others lives? It's only been a few hours and it's killing me. I feel like my heart's been ripped out of my chest.