I am a physics grad student and several of my professors have stated that they are against the idea of posting answer keys (i.e., worked solutions) for homework and/or tests (after the assignment has been completed by the student, of course). Their argument is that having an "answer cheat sheet" discourages the student from thinking critically about the problem and presents the opportunity for students to feel like they understand how to solve a problem without actually going through the rigor themselves. In fact, the entire department apparently takes the same stance with regards to posting past qualifying exams online: they post the past exams to use for studying, but not answer keys.
My question: Does any published education research (specifically for the math/physics fields) examine the pedagogical benefits and downsides of posting answer keys/worked solutions for students? I tried searching for this online, but had little success finding anything. If anyone could point me toward legitimate research on this topic, I'd appreciate it.
I should add that I was a high school physics teacher for two years, and within that arena it seemed unanimously accepted that making solutions and answer keys available was the right educational strategy. Hence my skepticism of my professors'/department's rationale. But I'm willing to see what the research says!