Quantum Mathematical Physics

The first part is devoted to quantum mechanics and especially to its applications to scattering theory, atoms and molecules. The second part deals with quantum statistical mechanics examining fundamental concepts like entropy, ergodicity and thermodynamic functions.Quantum Mathematical Physics: Atoms, Molecules and Large Systems

Thirring presents a logical mathematical foundation for quantum physics. This book is meant for theorists who desire a rigorous presentation and who already have a strong math background, especially in functional analysis. Naturally, much of the discussion centres on the properties of a Hilbert space (ie. a complete inner product space). Simpler texts in quantum mechanics might often state that the wavefunctions or operators reside in a Hilbert space, but really don't explore more the consequences. Whereas Thirring takes you much deeper into this realm.