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There are many (too many?) textbooks that cover the material of this course
at an appropriate level. You should find one whose style suits you. The lecture notes contain references to the following
books:
R. Shankar,
Principles of Quantum Mechanics, 2nd ed.
(Springer, 1994)
Shankar's approach is probably the closest to this course. The book is comprehensive and includes a good chapter on vector spaces.
F. Mandl, Quantum Mechanics (John Wiley, 1992)
This is part of the Manchester Physics Series; it is available as an ebook.
S. Gasiorowicz, Quantum Physics, 3rd ed.
(Wiley, 2003)
I have used Gasiorowicz's book frequently. I like his treatment of many of the applications of quantum mechanics.
D. J. Griffiths, Introduction to Quantum Mechanics,
2nd ed. (Cambridge, 2017)
A 3rd edition (2018) is now available, written by D. J. Griffiths and D. F. Schroeter.
That has added material on magnetic interactions and symmetries which will be relevant for PHYS40202 Advanced Quantum Mechanics. Chapters 1 to 5 and 12 cover the same material in both editions; chapters 6 to 8 in the 2nd edition correspond to chapters 7 to 9 in the 3rd.
There are also various sets of extensive on-line notes on quantum mechanics.
The following are at the right level. Both go further than this course and
will be useful for Advanced Quantum Mechanics as well.
Prof Richard Fitzpatrick, University of
Texas at Austin: Quantum Mechanics (UG)
and Quantum Mechanics (PG)
The UG notes start at the level of our PHYS20101 course.
The PG notes are more in the style of
this course and they cover vector spaces.
Prof Jim Branson of the University of
California San Diego: Quantum Physics
These also start at the beginning.
For revision of vector spaces, Shankar and Griffiths both cover the material; in addition the following on-line notes are at roughly the right level:
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