- In mathematics, an
antiunitary transformation is a
bijective antilinear map U:H1→H2{\displaystyle U:H_{1}\to H_{2}\,}
between two
complex Hilbert spaces...
- also
called a
unitary operator. A
closely related notion is that of
antiunitary transformation,
which is a
bijective function U : H 1 → H 2 {\displaystyle...
-
quantum mechanics, the time
reversal operation is
represented by an
antiunitary operator T : H → H {\textstyle T:{\mathcal {H}}\to {\mathcal {H}}} acting...
-
absolute value of the
inner products can be
represented by a
unitary or
antiunitary transformation of
Hilbert space,
which is
unique up to a
phase factor...
-
unitary operator, S = U, or an
antiunitary one, S = UK
where U is unitary, and K
denotes complex conjugation.
Antiunitary operators arise in
quantum mechanics...
-
direction of time. So
every antiunitary symmetry in a
theory with
positive energy must
reverse the
direction of time.
Every antiunitary operator can be written...
- laws in
quantum mechanics, the
requisite automorphisms are
unitary (or
antiunitary)
linear transformations of the
Hilbert space V.
Under Galilean relativity...
- and isometric. (Use
Polarization identity to show the only if part.)
Antiunitary –
Bijective antilinear map
between two
complex Hilbert spacesPages displaying...
- are linear,
unitary operators, T {\displaystyle T} is
antilinear and
antiunitary, ⟨ Ψ | T Φ ⟩ = ⟨ Φ | T − 1 Ψ ⟩ {\displaystyle \langle \Psi |T\,\Phi \rangle...
-
transformation is
represented by a
linear and
unitary or
antilinear and
antiunitary transformation of
Hilbert space. The
representation of a
symmetry group...
