It is often taught with a second course heavily focused on perturbation theory regarding Stark/Zeeman etc effects on the hydrogen atom. Finite dimensional Hilbert spaces are mostly regarded as spin which needs to get coupled to angular momentum for spin-orbit coupling. So I would envision a branching course sequence. An introductory course as we already have it followed by either or both of a usual second semester course for people who want the stuff for atoms and molecules or the one that sticks to the finite dimensional aspects that are relevant for computing. The physicists might need all 3 while the quantum computer scientists might only need the 2. Can be cross listed across departments.