Born’s rule is sometimes assumed to follow from Gleason’s theorem, which deduces the dependence of probabilities exclusively on the square of the norm, from the absence of any non-trivial alternatives. Indeed, if probabilities do depend on wave functions only, then the Born rule is the only reasonable outcome. But this is no derivation of quantum logic itself, and, as happens more often with purely mathematical theorems, any clues it might give concerning the nature of quantum mechanics itself, are misleading.
这里要说明，有人以为波函数总在 里，这是不正确的。 的domain小于 。 如果考虑平面波等散射态波函数，就要在rigged Hilbert space里说事。简单复读一下L2还是不够的。
2. 奉劝这个问题下所有回答的人，多看点Arxiv。波函数的塌缩有Rev. Mod. Phys. 讲：
It is often claimed that the collapse of the wave function and Born’s rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schro ̈dinger equation. Here we show that this is not true in certain models where quantum behavior can be attributed to underlying deterministic equations. It is argued that indeed the apparent spontaneous collapse of wave functions and Born’s rule are features that strongly point towards determinism underlying quantum mechanics.