The course will not follow any particular book. Any of the following books (which can be found in the Chemistry Library) covers the bulk of the course material and should provide a valuable supplement to class notes:

R. Shankar, “Principles of Quantum Mechanics”, Plenum.
A. Goswami, “Quantum Mechanics”, Wm. C. Brown Publishers.
J. J. Sakurai, “Modern Quantum Mechanics”, Addison–Wesley.
S. J. Jang, “Quantum Mechanics for Chemistry”, Springer.

For further reading, the following books are excellent choices:
G. M. Baym, “Lectures on Quantum Mechanics”, The Benjamin/Cummings Publishing Company.
K. Gottfried, “Quantum Mechanics: volume I”, The Benjamin/Cummings Publishing Company.
L. I. Schiff, “Quantum Mechanics”, McGraw–Hill.
L. D. Landau and E. M. Lifshitz, “Quantum Mechanics”, Pergamon Press.