Can you write someone smarter than you?

I have a character who's a psychiatrist. He's smart. He knows the human mind, knows how to question, knows how to pry information out of someone. His logic and intelligence is a kind of foil to my teenage protagonist, who is angry, mixed-up, and feels like she doesn't understand anything. There's a lot riding on the psychiatrist character working.
Trouble is he is way, way smarter than me. I've had to do a lot of research in writing him. I've read a lot of transcripts from therapy sessions to get a sense of delivery and cadence. I've read psychology books about how to coach someone through trauma. And I've watched a ton of episodes of Bones featuring the brainy and precocious FBI psychologist, Dr. Sweets. But, even taking all my research into consideration, I'm still wondering if it's actually possible to write someone that much smarter than you.
I watched an interview with Jim Parsons, the actor who plays the brainest person on TV, Dr. Sheldon Cooper from The Big Bang Theory. Even though Jim Parsons does seem pretty smart in real life, I suppose we can assume he isn't as smart as Sheldon because, well, nobody is. Parsons says his goal is to convey emotion in Sheldon's science-y speak, since Sheldon is incapable of expressing emotion any other way. I guess to Jim Parsons, the literal meaning of his lines isn't as important as the subtext--what it means for the character. He pulls it off brilliantly. That's kind of where I'm at right now with my psychiatrist. I understand him as a person, which is probably the biggest hurdle. Intelligence is one aspect of his character, but not all.

Do you think it's possible to write someone smarter than you? How would you go about doing that?