Starting out...
Hi
My first <interesting> exposure to quantum mechanics was through Feynman's lectures and a very limited amount of atomic structure course we had in school, when we read just about four lines about the wave equation.
Back then of course, the Schroedinger Wave Equation looked pretty complicated even with the concise H(psi) = E*psi representation! However, it seems you can go learn quite a bit without complex mathematical techniques, by actually getting a physical feel of things. For instance, it is not necessary to solve the wave equation for the hydrogen atom in general and understand everything about it in one shot--the Lagueere and Legendre Polynomials and the spherical harmonics for instance.
With every field of science, mathematical formalism is a must though but since we are not yet adept to handle transforms, complex integrals or polynomials which we have no basic idea about, reading from a book like Dirac's would put off the interested student since it gets too deep into mathematics as was pointed out on this thread earlier. At first sight, the mathematics looks complex and possibly stultifying especially to those who have not had much grounding in it before.
Hence, I highly recommend reading first from some elementary textbook to understand the basic ideas (without mathematics except possibly that of the coulombic and bohr models and quantum numbers) and get a feel of the physics involved before delving into a text that deals with the subject in a greater depth.
I began reading basic quantum theory from an old chemistry book (Theoretical Inorganic Chemistry by Marion Clyde, Day). I still am reading this book with simpler books like Grant and Phillips. Of course, references to advanced texts are necessary at times not only for clarification but also satisfaction.
As for the mathematics, I recommend that you become familiar with the "basics", which include vectors, complex numbers (a bit), coordinate systems and transforms (particularly spherical coordinates), the div, curl, grad, laplacian operators, their properties and their physical and geometric signifance. Next, a treatmeant (not necessarily overly mathematical again) of mechanical waves helps (and if you have had some EM wave courses, it helps too). Once these ideas are fixed and you feel comfortable using (and playing with) mathematical expressions involving them, you can start reading a book on quantum physics which talks about physics more, rather than mathematics alone. Leave some part of the math initially. Accept it in fact and go on. Don't get sidetracked by it. You can always come back to it once you begin to understand the formalism...it comes naturally once you begin to understand the physics.
Make notes, think about the ideas and look at your equations again and again. Try to visualize the situation in your mind without the equations first and let the parameters justify your reasoning, not the other way round.
This approach has helped me tremendously in not only this particular subject but also general physics over the past few weeks/months and hence I have emphasized more on the physics than (at first) the mathematics.
And of course, we all would get a chance to read it more thoroughly in college :-)
Hope you have a nice time with (quantum) mechanics/physics...
Cheers
Vivek
