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Longer titles found: Angular momentum operator (view)

searching for Momentum operator 55 found (168 total)

Quantum nondemolition measurement (1,080 words) [view diff] exact match in snippet view article find links to article

p2/2m. Because the Hamiltonian of the free particle commutes with the momentum operator, a momentum eigenstate is also an energy eigenstate, so once momentum

Angular momentum coupling (2,234 words) [view diff] exact match in snippet view article find links to article

quantum mechanical sense) in isotropic space. In both cases the angular momentum operator commutes with the Hamiltonian of the system. By Heisenberg's uncertainty

Complete set of commuting observables (3,851 words) [view diff] exact match in snippet view article find links to article

components are all compatible. Similarly, the Cartesian components of the momentum operator p {\displaystyle \mathbf {p} } , that is p x {\displaystyle p_{x}}

Quantum mechanics (12,087 words) [view diff] exact match in snippet view article find links to article

operators. The position operator X ^ {\displaystyle {\hat {X}}} and momentum operator P ^ {\displaystyle {\hat {P}}} do not commute, but rather satisfy

Algebraic quantum field theory (1,190 words) [view diff] exact match in snippet view article find links to article

spectrum S p ( P ) {\displaystyle \mathrm {Sp} (P)} of the energy-momentum operator P {\displaystyle P} (i.e. the generator of space-time translations)

Aharonov–Bohm effect (5,767 words) [view diff] exact match in snippet view article find links to article

electromagnetic field one can come close by declaring the eigenfunction of the momentum operator with zero momentum to be the function "1" (ignoring normalization

Ehrenfest theorem (2,833 words) [view diff] exact match in snippet view article find links to article

will have time dependence, the momentum operator itself, p does not, in this picture: Rather, the momentum operator is a constant linear operator on

Bioctonion (474 words) [view diff] exact match in snippet view article find links to article

V. Dzhunushaliev (2008) "Nonassociative decomposition of angular momentum operator using complex octonions", presentation at a meeting of the American

Schrödinger picture (1,469 words) [view diff] exact match in snippet view article find links to article

reflected in the state vector | ψ ⟩ {\displaystyle |\psi \rangle } , the momentum operator p ^ {\displaystyle {\hat {p}}} , or both. All three of these choices

Quantum mechanics of nuclear magnetic resonance spectroscopy (836 words) [view diff] exact match in snippet view article find links to article

Hamiltonian contains an angular momentum operator. So it will be easy if we find the eigenvalues of the angular momentum operator first and then substitute

London equations (2,157 words) [view diff] exact match in snippet view article find links to article

{s}}\right)} is defined by dividing the gauge-invariant, kinematic momentum operator by the particle mass m. Note we are using − e {\displaystyle -e} as

Schrödinger equation (10,263 words) [view diff] exact match in snippet view article find links to article

Hamiltonian is the sum of a kinetic-energy term that is quadratic in the momentum operator and a potential-energy term: i ℏ d d t | Ψ ( t ) ⟩ = ( 1 2 m p ^ 2

Superspace (2,266 words) [view diff] exact match in snippet view article find links to article

}C} where P = i ∂ μ {\displaystyle P=i\partial _{\mu }} is the 4-momentum operator. Again the covariant derivative is defined like the supercharge but

Riemann–Silberstein vector (2,015 words) [view diff] exact match in snippet view article find links to article

is the projection of its spin 1 onto its momentum since the normal momentum operator appears there from combining parts of rotations. In contrast to the

Kinetic energy (6,065 words) [view diff] exact match in snippet view article find links to article

in the Hamiltonian and is defined in terms of the more fundamental momentum operator p ^ {\displaystyle {\hat {p}}} . The kinetic energy operator in the

Quantum state (5,551 words) [view diff] exact match in snippet view article find links to article

momentum of 1 kg⋅m/s if and only if one of the eigenvalues of the momentum operator is 1 kg⋅m/s. The corresponding eigenvector (which physicists call

Coalgebra (2,899 words) [view diff] exact match in snippet view article find links to article

|A\rangle \otimes |B\rangle } . This is provided by the total angular momentum operator, which extracts the needed quantity from each side of the tensor product

Van Hove singularity (1,416 words) [view diff] exact match in snippet view article find links to article

is the vector potential and p → {\displaystyle {\vec {p}}} is the momentum operator. The density of states which appears in the Fermi's Golden Rule expression

Magnetic dipole transition (683 words) [view diff] exact match in snippet view article find links to article

vector potential of the wave and P {\displaystyle \mathbf {P} } is the momentum operator. The Hamiltonian can be split into a time independent and a time dependent

Relativistic angular momentum (10,985 words) [view diff] exact match in snippet view article find links to article

spin and this is an additional contribution to the orbital angular momentum operator, yielding the total angular momentum tensor operator. In any case

Cubic harmonic (2,031 words) [view diff] exact match in snippet view article find links to article

)} are the spherical harmonics, which are solutions of the angular momentum operator. The spherical harmonics are representations of functions of the full

Molecular Hamiltonian (5,204 words) [view diff] exact match in snippet view article find links to article

{P}}_{\alpha }} is the α component of the body-fixed rigid rotor angular momentum operator, see this article for its expression in terms of Euler angles. The

Spin–orbit interaction (4,419 words) [view diff] exact match in snippet view article find links to article

To find out what basis this is, we first define the total angular momentum operator J = L + S . {\displaystyle \mathbf {J} =\mathbf {L} +\mathbf {S}

Introduction to the mathematics of general relativity (3,180 words) [view diff] exact match in snippet view article find links to article

Spherical tensor operators are the eigenfunctions of the quantum angular momentum operator in spherical coordinates Diffusion tensors, the basis of diffusion

Introduction to the mathematics of general relativity (3,180 words) [view diff] exact match in snippet view article find links to article

Spherical tensor operators are the eigenfunctions of the quantum angular momentum operator in spherical coordinates Diffusion tensors, the basis of diffusion

Hartree–Fock method (4,739 words) [view diff] exact match in snippet view article find links to article

electrons. Typically, relativistic effects are completely neglected. The momentum operator is assumed to be completely non-relativistic. The variational solution

Optical phase space (2,494 words) [view diff] exact match in snippet view article find links to article

looks very similar to the commutation relation of the position and momentum operator. Thus, it can be useful to think of and treat the quadratures as the

X-ray photoelectron spectroscopy (6,255 words) [view diff] exact match in snippet view article find links to article

\nabla \cdot \mathbf {A} =0} ), the vector potential commutes with the momentum operator ( [ p ^ , A ^ ] = 0 {\displaystyle [\mathbf {\hat {p}} ,\mathbf {\hat

Configuration state function (1,690 words) [view diff] exact match in snippet view article find links to article

atomic structure, a CSF is an eigenstate of the square of the angular momentum operator, L ^ 2 {\displaystyle {\hat {L}}^{2}} the z-projection of angular

Berry connection and curvature (2,556 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbf {r} } . Due to translational symmetry, the momentum operator p ^ i {\displaystyle {\hat {p}}_{i}} could be replaced with m ℏ ∂

Atomic orbital (10,943 words) [view diff] exact match in snippet view article find links to article

{\displaystyle m=0} orbitals where are eigenstates of the orbital angular momentum operator, L ^ z {\displaystyle {\hat {L}}_{z}} . The columns with m = ± 1

Canonical quantization (4,736 words) [view diff] exact match in snippet view article find links to article

Likewise, the eigenstates | p ⟩ {\displaystyle |p\rangle } of the momentum operator P ^ {\displaystyle {\hat {P}}} specify the momentum representation:

Density functional theory (10,626 words) [view diff] exact match in snippet view article find links to article

V = −eZ/r is the Coulomb potential of a pointlike nucleus, p is a momentum operator of the electron, and e, m and c are the elementary charge, electron

Spinors in three dimensions (2,626 words) [view diff] exact match in snippet view article find links to article

\hbar ,...,+(S-1)\cdot \hbar ,+S\cdot \hbar } . The total angular momentum operator, J → {\displaystyle {\vec {\mathbb {J} }}} , of a particle corresponds

S-matrix (9,213 words) [view diff] exact match in snippet view article find links to article

this follows that the asymptotic states are all eigenstates of the momentum operator Pμ, P μ | i , k 1 … k m ⟩ = k 1 μ + ⋯ + k m μ | i , k 1 … k m ⟩ ,

Moment of inertia (17,179 words) [view diff] exact match in snippet view article find links to article

object. Alternatively it can also be written in terms of the angular momentum operator [ r ] x = r × x {\displaystyle [\mathbf {r} ]\mathbf {x} =\mathbf

Photon polarization (4,988 words) [view diff] exact match in snippet view article find links to article

\left(i\alpha _{x}-is\theta \right)|s\rangle \right].} The spin angular momentum operator is l ^ z = ℏ S ^ d . {\displaystyle {\hat {l}}_{z}=\hbar {\hat {S}}_{d}

Virial theorem (7,682 words) [view diff] exact match in snippet view article find links to article

_{n}{\frac {P_{n}^{2}}{2m_{n}}}} with the position operator Xn and the momentum operator P n = − i ℏ d d X n {\displaystyle P_{n}=-i\hbar {\frac {d}{dX_{n}}}}

Fermi's golden rule (3,948 words) [view diff] exact match in snippet view article find links to article

and mass of an electron, and p {\displaystyle {\textbf {p}}} is the momentum operator. Here we consider process involving one photon and first order in

Magnetic circular dichroism (4,686 words) [view diff] exact match in snippet view article find links to article

X} , L z {\displaystyle L_{z}} is the z {\displaystyle z} angular momentum operator, S z {\displaystyle S_{z}} is the z {\displaystyle z} spin operator

Diabatic representation (4,002 words) [view diff] exact match in snippet view article find links to article

is Hermitian and pure-imaginary. The off-diagonal elements of the momentum operator satisfy, ⟨ φ 2 | ( P A α φ 1 ) ⟩ ( r ) = ( P A α γ ( R ) ) + ⟨ χ 2

LSZ reduction formula (6,613 words) [view diff] exact match in snippet view article find links to article

(x)=e^{iP\cdot x}\varphi (0)e^{-iP\cdot x}} where Pμ is the four-momentum operator, we can write: e − i p ⋅ x ⟨ 0 | φ ( 0 ) | p ⟩ = Z e − i p ⋅ x ⟨ 0

Helium atom (5,941 words) [view diff] exact match in snippet view article find links to article

rotationally invariant, the total x, y or z component of angular momentum operator also commutes with the Hamiltonian. From these commutation relations

Joos–Weinberg equation (2,217 words) [view diff] exact match in snippet view article find links to article

(−i∂/∂t, ∇ ). Also Jeffery uses collects the x and y components of the momentum operator: p± = p1 ± ip2 = px ± ipy. The components p± are not to be confused

Nilsson model (1,439 words) [view diff] exact match in snippet view article find links to article

the spherical basis, ℓ {\displaystyle \ell } is the orbital angular momentum operator, ℓ 2 {\displaystyle \ell ^{2}} is its square (with eigenvalues ℓ (

Dynamical pictures (3,911 words) [view diff] exact match in snippet view article find links to article

sinusoidal oscillation should be reflected in the state vector |ψ⟩, the momentum operator p ^ {\displaystyle {\hat {p}}} , or both. All three of these choices

Gross–Pitaevskii equation (4,516 words) [view diff] exact match in snippet view article find links to article

{L}}=-i\hbar {\frac {\partial }{\partial \theta }}} is the angular-momentum operator. The solution for condensate wavefunction Ψ ( r , t ) {\displaystyle

Light front quantization (12,723 words) [view diff] exact match in snippet view article find links to article

modulus k = | k → | {\displaystyle k=|{\vec {k}}|} . The angular momentum operator reads: J → = − i [ k → × ∂ k → ] {\displaystyle {\vec {J}}=-i[{\vec

Representation theory of the Lorentz group (19,763 words) [view diff] exact match in snippet view article find links to article

spin 0 subspaces of dimension 3 and 1 respectively. Since the angular momentum operator is given by J = A + B, the highest spin in quantum mechanics of the

Quantum LC circuit (6,688 words) [view diff] exact match in snippet view article find links to article

|a|^{2}\ } . In the quantum case we have the following definition for momentum operator: p ^ = − j ℏ ∂ ∂ q {\displaystyle {\hat {p}}=-j\hbar {\frac {\partial

Peierls substitution (3,446 words) [view diff] exact match in snippet view article find links to article

m\vert } can be written explicitly using its generator, that is the momentum operator. Under this representation its easy to expand it up to the second

Gray molasses (2,408 words) [view diff] exact match in snippet view article find links to article

{\displaystyle |\psi _{\mathrm {nc} }(p)\rangle } are not eigenstates of the momentum operator, and thus motionally couple to one another via the kinetic energy

Multipole radiation (6,806 words) [view diff] exact match in snippet view article find links to article

{L} =-i\mathbf {x} \times {\boldsymbol {\nabla }}} is the angular momentum operator with the property L 2 Y ℓ m = ℓ ( ℓ + 1 ) Y ℓ m {\displaystyle L^{2}Y_{\ell

Oscillator representation (21,532 words) [view diff] no match in snippet view article find links to article

functions on R. Following the terminology of quantum mechanics, the "momentum" operator P and "position" operator Q are defined on S {\displaystyle {\mathcal

Lie algebra extension (17,708 words) [view diff] exact match in snippet view article find links to article

annihilation operator. (If it is zero, it is proportional to the total momentum operator.) Since the light cone plus and minus modes were expressed in terms