Complication of complex numbers being involved, but not getting students to really grapple with the technicalities of solving
Can mention Feynman sum of paths formalism, but this might be a bit too much for many students
Matrices and state vectors are powerful and more modern, simpler... maybe better to reserve it for university courses
Spin-statistics theorem is great, but maybe too advanced, though would be a good example to highlight the deep interconnections across areas of physics (some idea of angular momentum would be important pre-requisite though)
Should anyway introduce Maxwell distribution of classical particles before fermion/boson distributions