With respect to such a unitary representation, a symplectomorphism in the classical theory would now deform to a ( metaplectic ) unitary transformation.
22.
Unitary operators preserve inner products which means probabilities are also preserved, so the quantum mechanics of the system is invariant under unitary transformations.
23.
Unlike the convention followed in this article, when the Fourier transform is defined this way, it is no longer a unitary transformation on.
24.
Therefore, the concept of conformal transformations is itself transformed, and one arrives at the concept of a unitary transformation of a Hilbert space.
25.
The "'Schrieffer Wolff transformation "'is a unitary transformation enabling one to obtain J . R . Schrieffer and P . A . Wolff.
26.
Operators and state vectors in the interaction picture are related by a change of basis ( unitary transformation ) to those same operators and state vectors in the Schr�dinger picture.
27.
In the above derivation, the unitary transformation that is the change of basis ( from the standard product basis into the Bell basis ) can be written using quantum gates.
28.
Equations that apply in one picture do not necessarily hold in the others, because time-dependent unitary transformations relate operators in one picture to the analogous operators in the others.
29.
A physical system is generally described by three basic ingredients : one-parameter group of unitary transformations on the Hilbert space of states, and physical symmetries are realized by unitary transformations.
30.
A physical system is generally described by three basic ingredients : one-parameter group of unitary transformations on the Hilbert space of states, and physical symmetries are realized by unitary transformations.
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