So I've took a first undergrad quantum mechanics course and found it to be very dissatisfactory to say the least. We covered roughly the same material as classical textbook like Griffiths. I understand the abstract mathematical formulation of elementary quantum mechanics and find it very interesting as a mathematical theory. I find it very exciting that abstract mathematical topics like spectral theory of unbounded operators or distribution theory have concrete applications in describing the world we live in.
However, I don't really see why this whole quantum mechanics business is actual physics and helps us describe the "real world". Every quantum mechanics textbook (and the course I took) I looked at had the same structure: First, the need for a new theory beyond classical mechanics is presented by examples like the ultraviolet catastrophe, the electron falling into the nucleus, the Compton scattering and so on. This is fine. Then for me the disconnect happens: The abstract formulation of quantum mechanics modelled by Hilbert spaces and operators acting on them is "introduced" and the author goes on a rampage calculating different theoretical models like the particles in various potentials or finding eigenvalues of pertubed Hamilton operators. In this nightmare of calculations various phenomena like discrete energy values, tunneling or wave functions of entangled particles show up and through all of this one is supposed to "understand quantum mechanics". However, for me all of this provides little insight into why we expect this abstract formulation of quantum mechanics to describe reality in some way in the first place.
I understand that ultimatively a physical theory is just a tool describing reality (whatever that is) and if the theoretical predictions match the experimental results closely enough, the theory is considered "valid". But physics seems to me to be much more than using the tools some genius like Schrödinger or Dirac came up with and using them to separate the Schrödinger equation of a particle in some fictional potential. I want to know why and how they came up with these theories in the first place and what the physical intuition behind them is.
Sorry if this comes across as a bit of a rant on physics pedagogy, but I think this helps to understand better what sort of literature I'm looking for. I'm looking for a book that aims to give som insight into the physical intuition behind the abstract formulation of quantum mechanics. I can imagine two different interesting approaches:
- Following the historical development of quantum mechanics and explaining what various problems the physicists involved had to solve and why they did it the way they did (I mean Dirac won't have woken up one night and thought "Physical observables correspond to unbounded self-adjoint operators on a separable complete inner product space over the complex numbers!").
- Comparing the results of various real-world experiments with the results given by theoretical calculations and explaining why the formulation and axioms of quantum mechanics have to be chosen in exactly this way to match the experimental results.
I hope the text above helps in describing what sort of text I'm looking for.