I think it's possible to start with Shroedinger's equation as an axiom, and then quickly move on to probabilities. Griffith's table of content goes: 1.1 Shroed

I think it's possible to start with Shroedinger's equation as an axiom, and then quickly move on to probabilities. Griffith's table of content goes: 1.1 Shroedinger's equation 1.2 The statistical interpretation 1.3 Probabilities 1.4 Normalization ... 2.1 Stationary states 2.2 The infinite square well 2.3 The Harmonic oscillator 2.4 The Free Particle ... 3. Formalism 3.1 Linear algebra 3.2 Function spaces ... 4. Quantum mechanics in 3 dimensions 4.2 The hydrogen atom The problem with spin states is that it's too abstract for a lot of student, even though the math is simpler. Both approaches have merit, IMO. I find the square well + free particle to be much more interesting.