I'm looking for counterexamples in quantum theory, in the spirit of books like Counterexamples in topology and Counterexamples in analysis. A practically identical post, but for PDEs, can be found here.
This request will probably be clearer to people who have read those books: I am not looking for claimed 'disproofs' of quantum theory by cranks, but rather examples from quantum theory that defy intuition or expectation, or which 'break' theorems that we would otherwise want to hold, and in the process help clarify some of the theory's more subtle issues. Also note that I am not looking for ways in which quantum theory deviates from classical physics, like the tunneling effect or the blackbody spectrum.
A good example might be a strange solution to the Schrodinger equation, or to the Dirac equation in a particular field, or maybe something like the Haag–Lopuszanski–Sohnius theorem, etc.