Transitioning from Electrical Engineering to Applied Physics/Material Science So I have a bit of a dilemma. I'm an American. I graduated with a BS in Electrical Engineering and worked for the past two years in the RF field. I'm heading to school this fall to get my Master's. A somewhat unusual step, but I want to gently re-enter academia and improve my chances at getting into a good Ph.D program (Undergrad was good, but not spectacular). Overall my goals are:

&quot;Master&quot; Classical Electromagnetism
Learn semiconductor device design and fabrication
Get publications (I will be working with metamaterials)

Essentially I want to master the classical side of physics, dip my toe into quantum physics, and then for my PhD do research in solid state/device physics. The closer to basic science I get, the better. My university has plenty of classes on the semiconductor device design/fabrication and I know how I can fit that into my schedule. The problem is:

Can I apply to an Applied Physics program without filling the gaps in my physics knowledge prior to applying(stat. mech., solid state physics, et al.)?
Does the answer to question 1 change if I apply to a European university?
I won't comment on Europe.  The difference between a PhD in electrical engineering, applied physics, or solid state physics is often very small.  There is no reason not to try switching between those fields when you start your PhD.
To successfully apply for a PhD program, you should fill gaps in your knowledge.  You will likely need to obtain a good Physics GRE score and pass qualifying exams for programs in the US.  Exact practices vary, but you'll find most students have gaps in their knowledge that they need to fill.  Also, many of the students will have forgotten quite a bit of that material before they finish their PhDs.