So many entry-level explanations of quantum mechanics start with classical physics, waves, particles, the double-slit experiment, etc. and then jump straight to infinite-dimensional Hilbert spaces. In my opinion, there's way too much conceptual baggage that comes with these concepts [0].
As a non-physicist, QM only clicked for me when I learned the linear algebra of one- and two-qubit systems and observables on those systems [1]. The math is accessible at a pre-calculus level, and the most "counter-intuitive" aspects of QM (interference, the uncertainty principle, entanglement) make perfect sense in this framework. I think it's the best starting point for understanding what QM really says.
[0] That's not to say they aren't important historically or for a complete understanding of QM. I'm talking about conceptual understanding for someone, especially an amateur, encountering QM for the first time.
[1] Chapter 2 of Nielsen and Chuang is what did it for me. It's heavygoing if you've never seen linear algebra before, but I don't know of a clearer explanation of the postulates of quantum mechanics.
As a non-physicist, QM only clicked for me when I learned the linear algebra of one- and two-qubit systems and observables on those systems [1]. The math is accessible at a pre-calculus level, and the most "counter-intuitive" aspects of QM (interference, the uncertainty principle, entanglement) make perfect sense in this framework. I think it's the best starting point for understanding what QM really says.
[0] That's not to say they aren't important historically or for a complete understanding of QM. I'm talking about conceptual understanding for someone, especially an amateur, encountering QM for the first time.
[1] Chapter 2 of Nielsen and Chuang is what did it for me. It's heavygoing if you've never seen linear algebra before, but I don't know of a clearer explanation of the postulates of quantum mechanics.