not to be confused with Wigner classification
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Wigner’s theorem asserts that a function $f : H \to H$ from a Hilbert space to itself (not assumed to be a linear function)
is linear and in fact a (anti-)unitary operator (up to a phase) if only the function is
norm-preserving.
In quantum mechanics every symmetric operation needs to be a norm-preserving bijection from a Hilbert space of states to itself. Hence Wigner’s theorem asserts that in quantum mechanics symmetries are presented by unitary operators (or more rarely anti-unitary operator?s, as for example time reversal?).
Other theorems about the foundations and interpretation of quantum mechanics include:
See also
Last revised on December 28, 2017 at 17:36:57. See the history of this page for a list of all contributions to it.