Re: Mathematical Foundations of QM

Oh No <NotI@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
Thus spake curtvon@xxxxxxxxxxxxxx
could anyone recommend a book that tackles Quantum mechanical
mathematics? I am currently trying to do a little further reading
( currently testing out Shankar, Merzbacher and Landau- I have not yet
picked a favorite) and I want to know a little bit more about the
maths. (I'm a first year maths student but I am willing to work hard
given a good book).

Jauch, Foundations of Quantum Mechanics, is probably still the best
treatment for a mathematician.

Definitely a terrific book, but maybe a bit beyond a first-year
student. A similar undergraduate-level book is
An Introduction to Hilbert Space and Quantum Logic,
David W. Cohen, Springer-Verlag 1989, ISBN 0-387-96870-9

Given the variety of recommendations offered, the original poster
probably ought to know that there are several axiomatic approaches
to quantum mechanics. The traditional one is the Hilbert space
approach, followed by most textbooks, including those mentioned
by the o.p. and by Chris Isham's book that I recommended earlier.
Jauch's book and Cohen's book, recommended here, more closely
follow the quantum logic approach. But there's also the operational
statistics approach (which Cohen also develops), the convexity
approach, the algebraic approach, the hidden variables appraoch,
the coherent histories approach, and probably several others I've
failed to mention.
I recall reading a review article somewheres, that compares
and contrasts all these approaches, but can't find it or recall
its author or title. Maybe someone can chime in. And maybe the
o.p. might want to read something like that to better classify
and evaluate the variety of books he browses through.
--
John Forkosh ( mailto: j@xxxxx where j=john and f=forkosh )

.

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