mechanics, the position operator is the operator that corresponds to the position observable of a particle. When the position operator is considered with...

mechanics, the momentum operator is the operator associated with the linear momentum. The momentum operator is, in the position representation, an example...

In quantum mechanics, a translation operator is defined as an operator which shifts particles and fields by a certain amount in a certain direction. It...

statement is true for the position operator: when the system is rotated, the three different components of the position operator are effectively interchanged...

unit operator. In general, position and momentum are vectors of operators and their commutation relation between different components of position and momentum...

position operator are called the eigenkets and are denoted by φy = |y⟩. Similar considerations apply to any other (unbounded) self-adjoint operator with...

possible for an operator to have a non-discrete spectrum, such as the position operator X {\displaystyle X} in quantum mechanics. This operator has a completely...

angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role...

eigenfunctions of the position operator as a set of basis functions, one speaks of a state as a wave function ψ(r) in position space. The familiar Schrödinger...

into quantum mechanics, where it becomes an operator on a wave function. The momentum and position operators are related by the Heisenberg uncertainty principle...

The Global Positioning System (GPS) is a satellite-based hyperbolic navigation system owned by the United States Space Force and operated by Mission Delta...

a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which apply...

the position operator at time t. The above equation shows that the operator αk can be interpreted as the k-th component of a "velocity operator". Note...

operator with corresponding eigenvalue(s) E {\displaystyle E} ; the energy of the system. An example of the continuous case is given by the position operator...

has to take into account the position operator and its tensorial square. For a system of n electrons, the position operator and its Cartesian components...

Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study...

represented by Hermitian operators. The position operator X ^ {\displaystyle {\hat {X}}} and momentum operator P ^ {\displaystyle {\hat {P}}} do not commute...

the failure of one does not result in a loss of position. This is left to the judgment of the DP operator. For Class 2 and Class 3 a Consequence Analysis...

electric dipole moment: The sum of the positions, weighted by charge. If the ith particle has charge qi and position operator ri, then the transition dipole moment...

also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional...

In quantum mechanics, a density matrix (or density operator) is a matrix that describes an ensemble of physical systems as quantum states (even if the...

Theodore Duddell Newton and Eugene Wigner) is a scheme for obtaining a position operator for massive relativistic quantum particles. It is known to largely...

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...

{\hat {x}}} is the position operator (given by x in the coordinate basis), and p ^ {\displaystyle {\hat {p}}} is the momentum operator (given by p ^ = −...

of operator position, an operator may be prefix, postfix, or infix. A prefix operator immediately precedes its operand, as in −x. A postfix operator immediately...

{X}}|\psi \rangle =0} where X ^ {\displaystyle {\hat {X}}} is the position operator. For a state | L → , L z ⟩ {\displaystyle {\bigl |}{\vec {L}},L_{z}{\bigr...

the commutator relationship between the position operator x ^ {\displaystyle {\hat {x}}} and the momentum operator p ^ {\displaystyle {\hat {p}}} : [ p ^...

In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential...

"Smooth Operator" is a song by English band Sade from their debut studio album, Diamond Life (1984), and was co-written by Sade Adu and Ray St. John. It...

quantum position operator and p as the quantum momentum operator. L is then an operator, specifically called the orbital angular momentum operator. The components...