Is this enough background to begin QM\GR?

I have recently independently studied my way through Electrodynamics (Schwartz, Griffiths, and Shadowitz), Lagrangian\Hamiltonian formalism of Dynamics, about two books on special relativity, and a few books entailing mathematics for QM and GR. I did, however, skip through most of the parts on electromagnetic fields in matter and solving the laplace\poisson equations (I completely skipped bessel functions, harmonic functions, and legendre polynomials for brevity) to save time. My question is as follows: Is this background sufficient to move into QM and GR? I am wholly interested in the theoretical points of the theorems and not so much on the application (which is another reason I skipped the sections I did). I want to be able to understand QM and GR from a theoretical point of view and I am worried I have skipped too much to have a satisfactory understanding to move on to these subjects. Any suggestions would help.

Chris
 Yea that's enough. The more important thing to worry about IMHO is the textbook. I like Wald for GR and in your case since your are interested in the theory Hughs - The Structure And Interpretation Of QM prior to Ballentine - QM A Modern Development. Ballentine develops QM from two axioms and relegates, correctly, the Schodenger Equation etc to its true basis - a derivation from Galilean invariance. Thanks Bill
 Thanks Bill! I'm really excited to extend my knowledge to these fields and ready to start!

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Is this enough background to begin QM\GR?

cps...
I agree..you are 'good' to go'..have fun.
 Recognitions: Science Advisor Yep, you are good to go, and you'll see how wise your decision was not to learn about Bessel functions, spherical harmonics, etc. within classical physics. It's much more natural to get these issues covered within quantum theory, where you'll learn that all these functions are representations of orthonormal complete bases of the Hilbert space $\mathrm{L}^2$ of square-integrable functions. Have fun!
 If you're just beginning to study these subject then I recommend, as always, "a Modern Approach to Quantum Mechanics" by Townsend and "Gravity: An Introduction to Einstein's General Theory of Relativity" by Hartle. For the QM, you need linear algebra and series solutions to diff eqs. For GR, diff geo would be great but not really needed for Hartle since he develops what you need to know. I think after working through these books, you'll be comfortable to move onto graduate/advanced texts like Sakurai and Wald. Also, I would advise against picking up Griffiths for QM. It's not very formal and works mostly in position space, not developing the full dirac notation and therefore missing some great insights. Since you said you're more of a theory guy, then Townsend would be great.