Quantum Mechanics Algebras and Distributions

These notes present a rigorous mathematical formulation of quantum mechanics based on the algebraic framework of observables and states. The underlying mathematics is that of topological algebras, locally convex spaces and distribution theory. Amongst the topics considered is Dirac's bra and ket formalism. These notes also contain a discussion of quantum measurement theory, using the Copenhagen interpretation, but taking into account the algebraic structure and the phenomenon of continous spectra of observables.