For definiteness, I write, for the arbitrary vector $$\psi$$ that $$\psi = \sum_{jk}\alpha_j\varphi^j\alpha_k\varphi^k$$ (the $$\varphi$$ are the basis vectors, the $$\alpha$$ are scalars).

Now looking at the sum above, this looks awfully like a mathematical representation of so-called superposition of states. So my question is this: if this is correct, does that imply that most quantum systems are in superposition of what might be called "singular states" ?

And if it's not correct, what

*is*the basis for state space?