Error message
- Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: UpdateQuery::expression(): Implicitly marking parameter $arguments as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: MergeQuery::expression(): Implicitly marking parameter $arguments as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryInterface::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryInterface::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryExtender::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryExtender::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQuery::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQuery::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
Definition: In mathematics, an
operator is a function, that operates on (or modifies)
another function.
In the following, though, we will consider the use that is made of
operators in Quantum Mechanics and therefore focus upon particular
classes of operators or operators with certain properties.
In the absence of superselection rules the following two axioms hold
for any quantum system:
Axiom 1: The states of any physical system are in
one-to-one correspondence with the vectors of an abstract, separable,
infinite dimensional
Hilbert
space ℋ.
Axiom 2: Every dynamical variable 𝒜 of a quantum system can be represented by
an operator A in the Hilbert space of the
vector states, in the sense that the mean values of any dynamical
variable function of 𝒜 can be computed
as the mean values of the same function of the operator A.
In order to be considered an
observable
A must be a linear,
self-adjoint and
positive
operator.
In particular, A must be a
linear operator so that its mean values do not depend on the length of
the vector chosen to compute them; whereas A must be a
self-adjoint
operator to guarantee the reality, and thus the physical
consistency, of its mean values.
Category:Mathematical
Structure
Category:Handbook
of Quantum Information
Last modified:
Monday, October 26, 2015 - 17:56
