Plancherel's theorem makes it possible to extend the Fourier transform, by a continuity argument, to a unitary operator on.
32.
Every antiunitary operator can be written as the product of the time reversal operator and a unitary operator that does not reverse time.
33.
This version of the spectral theorem for self-adjoint operators can be proved by reduction to the spectral theorem for unitary operators.
34.
In other words, for any two such and acting jointly irreducibly on a Hilbert space, there is a unitary operator so that
35.
In general, a partial isometry may not be extendable to a unitary operator and therefore a quasinormal operator need not be normal.
36.
When the Hamiltonian is time-independent the unitary operator is e ^ {-i \ hat { H } t }.
37.
Unitary operators correspond to state changes without any wave function collapse . talk ) 21 : 32, 8 October 2008 ( UTC)
38.
Unitary operators preserve inner products which means probabilities are also preserved, so the quantum mechanics of the system is invariant under unitary transformations.
39.
Different ensembles describing the state " ? " are related by unitary operators, via the square roots of " ? ".
40.
Bundle P over M, where PU ( \ mathcal H ) is the group of projective unitary operators on the Hilbert space \ mathcal H.
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