"Our little angel, Sophie, is about to turn 11 months and she can never be left alone in her park or in another room without starting to scream until my wife or I go to be with her or to pick her up. I spend the week at the office, so I can get a break, but my wife is going crazy. Whenever I call her home to see how things are going, all I can hear is my daughter screaming in the back... I read that it's what's called "separation anxiety" and that we should stop running to pick her up when she screams... What do you suggest?"
I suggest earplugs.
Seriously, though, this is just the most annoying thing, isn't it? It makes you want to jump out of your skin and run far away to a land where everyone is mute.
I think it's counterproductive to ignore her when she screams. Separation anxiety is a normal thing for kids, and is part of the process of figuring out that they are not you and you are not them. The start to separate, then they need to pull back in to make sure you're not gone once she starts to walk away. So ignoring her is actually going to make this stage last longer.
The best thing would be to strap her to whoever is home in a sling or Ergo or other carrier. She can't get too freaked out if she's right there with you, and she might even get bored enough to want to go off on her own. If you can't stand that, though, and there's no shame in admitting it, see if you can just bring her from room to room with you. Set up the highchair in whatever room you're in, and let her play with stuff while you're working. One fun project for older babies is to take off their shirts and let them color all over themselves and the highchair tray with washable markers. It's a little messy, but it keeps them entertained because it's usually forbidden, and it washes right off.
If any neighbors have a preschooler, you might also try to borrow him or her for an hour. Babies love big kids (3-4-year-olds), and just like to watch them play. Babies will accept the presence of a kid, even when they'd be freaked out by another adult. Your neighbor will certainly appreciate it, and it might buy you some quiet time.
I'm sure some of the readers will have other suggestions for activities to keep her close enough to you not to freak out, but not right on top of you smothering you with her desire to jump into your skin. In the meantime, keep your chin up. It only lasts a few weeks, and then she'll be off and away from you. If you can stay sane until then you'll be home-free.