Book on Classical and Quantum Mechanics

[Reedeegi]

Is there a mathematically rigorous book that covers both classical and quantum mechanics? If so, what is the book?

[xepma]

You're better off getting two seperate books.

[Landau]

Depends on what you mean by 'mathematically rigorous'. E.g.
Ballentine (http://www.amazon.com/Quantum-Mechanics-Development-Leslie-Ballentine/dp/9810241054) for QM
Marsden (http://www.amazon.com/Foundations-Mechanics-AMS-Chelsea-Publishing/dp/0821844385/ref=sr_1_5?ie=UTF8&s=books&qid=1253626138&sr=1-5) or Arnol'd (http://www.amazon.com/Mathematical-Classical-Mechanics-Graduate-Mathematics/dp/0387968903/ref=pd_cp_b_1) for CM.

[Fredrik]

Ballentine is excellent, but it should be your third book on QM, not your first. Griffiths and Isham are good choices for the first two books. However, if you want want to see every relevant theorem stated and proved, you need to study some measure/integration theory and then functional analysis (e.g. Kreyszig or Sunder). After that, I suggest Strocchi.

[Pinu7]

How mathematically rigorous?

Classical Mechanics
Introductory: Mechanics: From Newton's Laws to Deterministic Chaos-Scheck
More advanced: Introduction to Mechanics and Symmetry- J.E. Marsden
Foundations of Mechanics- J.E. Marsden

Quantum Mechanics
Ballentine, as others mentioned
Introductory Quantum Mechanics-Liboff
Mathematical Foundations of Quantum Mechanics-Neumann

EDIT: Liboff is considered an introductory text but a much superior one than, let's say, Griffiths.