Fr.: opérateur d'annihilation
In → quantum field theory, the operator that lowers → eigenstates one → energy level, contrarily to the → creation operator.
→ annihilation; → operator.
Fr.: opérateur de création
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.
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.
Fr.: opérateur del
In → vector calculus,
a vector → partial derivative represented by the symbol
→ nabla and defined in three dimensions to be:
From Gk. alphabet letter delta.
Fr.: opérateur à quatre dimensions
An operator defined as: ▫ = (∂/∂x, ∂/∂y, ∂/∂z, 1/(jc∂/∂t).
→ four; → dimensional; → operator.
Fr.: opérateur hamiltonien
The dynamical operator in → quantum mechanics that corresponds to the → Hamiltonian function in classical mechanics.
→ Hamiltonian function; → operator.
Fr.: opérateur hermitien
An operator A that satisfies the relation A = A*, where A* is the adjoint of A. → Hermitian conjugate.
→ Hermitian conjugate; → operator.
Fr.: opérateur d'identité
An operator which takes a real number to the same real number.
Fr.: opérateur intégral
Math.: An operator whose inverse is a differential operator.
Fr.: opérateur de Laplace
Same as → Laplacian.
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.
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Fr.: opérateur en mécanique quantique
A linear → Hermitian operator associated with a physical quantity.
Fr.: opérateur unitaire
A linear operator whose inverse is its → adjoint. In addition to → Hermitian operators, unitary operators constitute a fundamentally important class of quantum-mechanical operators.