Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics which is
adjoint to itself
Etymologies
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Examples

Each bounded simple random variable f gives rise to a bounded selfadjoint operator A =

It is not difficult to show that a selfadjoint operator P with spectrum contained in the twopoint set {0,1} must be a projection; i.e.,

There remains to recover, e.g., the representation of “observables” by selfadjoint operators, and the dynamics (unitary evolution).

Studying the properties off these observations one sees that they satisfy the necessary axioms to be linear operators, and, in fact, selfadjoint operators.
Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask

Pauli pointed out that a (selfadjoint) time operator is incompatible with a Hamiltonian spectrum bounded below.

The observable quantities are represented by selfadjoint operators B on the Hilbert space.

This amounts to rejecting that for every selfadjoint operator, there is a welldefined observable.

If we further assume that to every selfadjoint operator there corresponds a QM observable, then the principle can be formulated thus:

The principle trades on the mathematical fact that for a selfadjoint operator A operating on a Hilbert space, and an arbitrary function f:

If the nonintrinsic, statedependent properties are identified with all the monadic or relational properties which can be expressed in terms of physical magnitudes associated with selfadjoint operators that can be defined for the particles, then it can be shown that two bosons or two fermions in a joint symmetric or antisymmetric state respectively have the same monadic properties and the same relational properties one to another (French and Redhead 1988; see also Butterfield 1993).
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