An Etymological Dictionary of Astronomy and Astrophysics
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In → quantum field theory, the operator that lowers → eigenstates one → energy level, contrarily to the → creation operator.

→ annihilation; → operator.

An operator that acts on the → eigenstate describing the → harmonic oscillator to raise its → energy level by one step. The creation operator is the → Hermitian conjugate operator of the → annihilation operator.

→ creation; → operator.

A second order, → partial differential operator in space-time, defined as: ▫² = ∂²/∂x² + ∂²/∂y² + ∂²/∂z² - (1/c²)∂²/∂t², or ▫² = ∇² - (1/c²)(∂²/∂t²), where ∇² is the → Laplacian and c is the → speed of light. This operator is the square of the → four-dimensional operator  ▫, which is Lorentz invariant.

→ d'Alembert's principle; → operator.

In → vector calculus, a vector → partial derivative represented by the symbol → nabla and defined in three dimensions to be:
∇ = (∂/∂x)i + (∂/∂y)j + (∂/∂z)k.
It appears in the operations → gradient: ∇f, → divergence: ∇ . E, → curl: ∇ x E, and → Laplacian: ∇ . ∇f = ∇²f.

From Gk. alphabet letter delta.

An operator defined as: ▫ = (∂/∂x, ∂/∂y, ∂/∂z, 1/(jc∂/∂t).

→ four; → dimensional; → operator.

The dynamical operator in → quantum mechanics that corresponds to the → Hamiltonian function in classical mechanics.

→ Hamiltonian function; → operator.

An operator A that satisfies the relation A = A^*, where A^* is the adjoint of A. → Hermitian conjugate.

→ Hermitian conjugate; → operator.

An operator which takes a real number to the same real number.

→ identity; → operator.

Math.: An operator whose inverse is a differential operator.

→ integral; → operator.

Same as → Laplacian.

→ Laplace; → operator.

Math.: Something that acts on another function to produce another function. In linear algebra an "operator" is a linear operator. In calculus an "operator" may be a differential operator, to perform ordinary differentiation, or an integral operator, to perform ordinary integration.

From → operate; + → -or.

A linear → Hermitian operator associated with a physical quantity.

→ quantum; → mechanics; → operator.

A linear operator whose inverse is its → adjoint. In addition to → Hermitian operators, unitary operators constitute a fundamentally important class of quantum-mechanical operators.

→ unitary; → operator.