[4/4]

> Base states are arbitrary things, like a trap or a goal in QMM, but you can still ask what the chances are of a particle being in one of them.

You're right that basis states can be arbitrary. However, that's not their most important characteristic. We say we have a basis if we have a set of states that covers all the possibilities and they're not redundant. That is, if any state can be written as a unique sum of basis states.

> Stationary states are more like wavefunctions in QMM that have settled into a stable condition. Their phase may go on changing, but the amplitude doesn’t.

The set of stationary states is a special basis. It's the set that when evolved in time only change by a phase, as you suggest---these states don't get mixed together when time marches on. So, how can a system "settle" into such a state? In other words, if you rewind the Schrodinger equation, what state was the system in before? Simple: it was in the same stationary state!

Because stationary states form a basis, any non-stationary state is a unique sum of stationary states. In fact, if you know this basis and their corresponding energies you know all there is to know about a system's dynamics! If you take an arbitrary state and decompose it as a sum over stationary states (which is always possible, since they form a basis) then you immediately know how that state evolves in time, because you know how the individual components evolve in time.

Since the individual stationary-state components don't mix together, the only thing that changes in time is their relative phases. So, if a system doesn't start in a stationary state, it cannot possibly reach one, without there being some kind of perturbation (ie. alteration of the system).

Postscriptum

Not having played, I can't say that it's not faithful to a deep understanding of quantum mechanics. But, I am skeptical, because your write-up seems to have a lot of confusion about what QM actually is / says. That's OK---it's a tricky subject. But I would avoid trying to push your game as a pedagogical learning tool unless it's been thoroughly vetted by actual physicists, because you could easily confuse neophytes.

In some sense, the learning approach you have laid out stresses the parts of quantum mechanics that are the least interesting and least novel---they can be understood from playing with a wave equation. What's new is superposition, commutation of operators (or failure to commute), interference. That's why most modern approaches start with two-state systems (which immediately require bras and kets) and only go to systems with spatial extent later. In other words, it's better pedagogically to understand the operating system (quantum mechanics) before you start studying particular programs (particular systems).

When you study particular systems there's a lot of intricate detail that doesn't matter for you to learn the lesson. You don't really need to know about the Laguerre polynomials or whatever. The way you learn quantum mechanics is by showing a bunch of wavefunctions are orthogonal---it's not about performing integrals. You're better off understanding orthogonality, linearity, and unitarity.

> I found myself baffled trying to understand the connection between state notation, continuous wavefunctions...

Moving from bras and kets to wavefunctions is, honestly, trivial---if you have a firm understanding of what's going on. That's why I'm nervous about trying to translate your game (which again, may be faithful to QM---I haven't played) into actual education.

[continuity] https://en.wikipedia.org/wiki/Continuity_equation#Quantum_me...

[isospin] https://en.wikipedia.org/wiki/Isospin

[fourplet] after triplet the words we use vary a bit. I've seen sextet, octet, and decuplet, but almost everything else is a n-plet or, generically, a multiplet.

[weak] https://en.wikipedia.org/wiki/Weak_isospin

Sorry about the multi-comment. When I tried to post it as one thing I just got "That comment was too long."