I would probably ere away from directly calling the physician. They're EXTREMELY busy most of the time and will more than likely be a little irritated you're taking up their work time and didn't just send them an email or contact someone in human resources. You could just do what I did and email the physician recruiter of the hospital you're looking at asking about job shadowing. The recruiter I emailed was really nice and not only offered chances to shadow the specialty I wanted, but a bunch of other specialties as well throughout the hospital. If you're not looking to shadow in a hospital setting, then call the front desk or email the place you would like to shadow and just ask about job shadowing. They'll know who you should get in touch with about job shadowing anesthesiologists, plastic surgeons, etc 🙂