<p>After doing a few internships, I’ve decided that I definitely want a career in research</p>
<p>That’s only half the battle, though, in being ready to apply to doctoral programs. If you’re asking whether or not you can switch departments from the outset it’s a sign that you’re not ready - not because you’re not worthy or something, but simply because you need to be settled on which department you’re going to apply to. That’s not to say that you have to apply to the same department at all universities - it’s not uncommon to apply to two different departments…at different schools. I had friends who for example applied to poli sci departments at some places and sociology at others.</p>
<p>You need to nail down what it is you’re interested in and what kind of approach you want to take to answering your questions. Your department won’t change the questions, just the approach. Do you want to answer questions like a physicist or like a mathematician? Look at the published papers in the subjects you’re interested in studying and see who’s taking approaches to them that you like.</p>
<p>From my perspective it looks like you’re interested in being a physicist who uses applied math to answer the questions, and that’s not uncommon. Find a physics department that’s big on interdisciplinary work and that will let you take classes in the math and comp sci departments to enrich your research.</p>
<p>Before you apply, you also need to narrow down your field to what you want to study - lasers, solids, fluids, etc. You can’t apply with a nebulous group of ideas; you need to sound focused.</p>