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An operator is a function over a space of physical states onto another space of states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context).
The momentum operator can be described as a symmetric (i.e. Hermitian), unbounded operator acting on a dense subspace of the quantum state space. If the operator acts on a (normalizable) quantum state then the operator is self-adjoint. In physics the term Hermitian often refers to both symmetric and self-adjoint operators. [7] [8]
The phenomenology of quantum physics arose roughly between 1895 and 1915, and for the 10 to 15 years before the development of quantum mechanics (around 1925) physicists continued to think of quantum theory within the confines of what is now called classical physics, and in particular within the same mathematical structures.
REDIRECT AP Physics 2; References This page was last edited ... This page was last edited on 2 January 2025, at 06:05 (UTC).
In quantum mechanics, energy is defined in terms of the energy operator, acting on the wave function of the system as a consequence of time translation symmetry. Definition [ edit ]
The CPT theorem appeared for the first time, implicitly, in the work of Julian Schwinger in 1951 to prove the connection between spin and statistics. [3] In 1954, Gerhart Lüders and Wolfgang Pauli derived more explicit proofs, [4] [5] so this theorem is sometimes known as the Lüders–Pauli theorem.
In quantum mechanics, a complete set of commuting observables (CSCO) is a set of commuting operators whose common eigenvectors can be used as a basis to express any quantum state.
Curl, (with operator symbol ) is a vector operator that measures a vector field's curling (winding around, rotating around) trend about a given point. As an extension of vector calculus operators to physics, engineering and tensor spaces, grad, div and curl operators also are often associated with tensor calculus as well as vector calculus.