For a (I assume
) tongue-in-cheek take on this, see Chris’s signature.
Physics is the study of matter and energy in the broadest sense. (The word “physics” itself has its roots in the Greek words “natural” and “nature”—as in “natural laws” or the “laws of nature.”) In this context, chemistry, as well as each of the other natural sciences, is a subset, or specialty area, of physics. Thus, one could legitimately say that chemistry and the other natural sciences each is an example of applied physics. (Note that since mathematics is the language of physics, one also could argue that physics is an example of applied mathematics.)
When you say that “the study of chemistry versus the study of quantum physics is characterized by a lack of math and a lack of understanding,” you are making a broad-brush statement that denigrates the science of chemistry and its practitioners. I’m willing to bet that there are areas of chemistry (as there are areas within any of the other areas of “applied physics”) that most physicists would be hard-pressed to tackle. Knowing (or not knowing) how to solve the Schrödinger Equation and self-consistent field equations certainly didn’t help Aaron Ciechanover, Avram Hershko, and Irwin Rose win their 2004 Nobel Prize for Chemistry, though I’m sure it was an important ingredient in the basic training of David J. Gross, H. David Politzer, and Frank Wilczeck that enabled that trio win theirs for Physics.