Byron and Fuller’s QM treatment.b
Posted by peeterjoot on April 24, 2010
I’d purchased the Dover book Mathematics-Classical-Quantum-Physics a while back, and set myself to reading some of the QM treatment in this book recently. Damn. With so much else in this book so eminently practical seeming (lots of details on special functions, complex numbers, green’s functions, …), I’d not expected such an abstract treatment of QM. This book takes an axiomatic approach, which I’ve seen in other places, but does so in the context of Hilbert space and Stieljes integrals, and the spectral theorem for self adjoint operators expressed in terms of an operator valued resolution of the identity (something roughly akin to a requirement to calculate a delta function for the operator). I have to admit that this is hard to get ones head around. For such an abstract treatment, there are really not enough problems for me to be able to grasp this well, and the ones that are included are a little too hard seeming. Understanding how to relate this to some of the much simpler QM treatments I’ve seen is also not clear.
I think this is something to revisit later after tackling QM in a more conventional, physics based way.