How to know if foundation is strong enough

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The discussion centers on a chemistry major contemplating graduate school in physical chemistry or condensed matter physics. The individual expresses concern about their foundational knowledge, particularly regarding key concepts like Lagrangian and Hamiltonian mechanics and Maxwell's equations, which are relevant to their interest in spectroscopy. Despite feeling underprepared, they acknowledge that PhD work often involves developing learning skills rather than just acquiring knowledge. To strengthen their background, the individual is considering adding a physics major to enhance their mathematical skills and maintain flexibility for potential physics graduate school applications. They seek clarity on the differences between regular and applied physics graduate programs, noting that both allow for research in condensed matter areas, and they inquire about the distinctions between condensed matter physics and atomic, molecular, and optical (AMO) physics. The conversation highlights the importance of self-assessment in academic readiness and the value of interdisciplinary study in preparing for advanced research.
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I'm a chem major in a similar situation as this fellow
https://www.physicsforums.com/showthread.php?t=422136

Anyway, I've completed the chemistry degree and am looking to do graduate school in physical chemistry/condensed matter physics (something I need to figure out is what's up with all these labels... and what I want to do specifically).
Talking to my professors and some graduate students, they've echoed two things:
1. "you know more then you realize"
2. "you have a degree, you're eligible for graduate school"

What I have trouble with is the idea that someone (ie me) who doesn't understand the difference between Lagrangian and Hamiltonian mechanics or has never used maxwell's equation (im interested in spectroscopy) could be starting a phd program.
At the same time though, I realize a great deal of phd work involves learning how to learn how to learn, and not just learning stuff.
So how do you know when you have a strong enough foundation? Obviously, there will always be something I don't know walking to a phd program (and even leaving it), but how does one gauge their standing?

Right now, I've penciled myself into stay my last years and pick up a physics major for two reasons:
1. to learn more math. specifically, the math taught in physics classes.
2. in case I want to go to physics graduate school instead of chemistry.
Anyone have any opinions?

also side questions:
whats the difference between regular physics and applied physics graduate school? I can still do research in condensed matter-ish areas and the classes are the same, what's up?

is there a clear distinction between condensed matter and AMO physics?
 
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