In quantum mechanics, the canonical commutation relation is the fundamental relation between canonical conjugate quantities (quantities which are related...

commutation matrix is used for transforming the vectorized form of a matrix into the vectorized form of its transpose. Specifically, the commutation matrix...

{\displaystyle \mathbb {C} } . The Pauli matrices obey the following commutation relations: [ σ j , σ k ] = 2 i ε j k l σ l , {\displaystyle [\sigma _{j}...

Let Q and P be two self-adjoint operators satisfying the canonical commutation relation, [Q, P] = i, and s and t two real parameters. Introduce eitQ and...

over F q {\displaystyle \mathbb {F} _{q}} , W. Feit and N. J. Fine showed the equation 1 + ∑ n = 1 ∞ P ( n ) ( q n − 1 ) ( q n − q ) ⋯ ( q n − q n − 1...

q ) , {\displaystyle f(q),} ( d d q q − q d d q ) f ( q ) = d d q ( q f ( q ) ) − q d f ( q ) d q = f ( q ) {\displaystyle \left({\frac {d}{dq}}q-q{\frac...

also addressed as q-Gaussian process, arising from free probability theory and corresponding to deformations of the canonical commutation relations. For...

q ∗ Q {\displaystyle T_{q}^{*}Q} . Here, X q {\displaystyle X_{q}} is a vector in T q Q {\displaystyle T_{q}Q} , the tangent space to the manifold Q at...

The commutation cell is the basic structure in power electronics. It is composed of two electronic switches (today, a high-power semiconductor, not a...

satisfying the commutation relation x y = q y x {\displaystyle xy=qyx} , then e q ( x ) e q ( y ) = e q ( x + y ) {\displaystyle e_{q}(x)e_{q}(y)=e_{q}(x+y)}...

This preserves the desired commutation relations in either real space or wave vector space [ x l , p m ] = i ℏ δ l , m [ Q k , Π k ′ ] = 1 N ∑ l , m e...

group isomorphism, which is a semidirect product of N and H, with the commutation of elements of N and H defined by φ {\displaystyle \varphi } . ≀ In group...

take P = QT. The matrices P and Q are perfect shuffle matrices, called the "commutation" matrix. The Commutation matrix Sp,q can be constructed by taking...

then Q. Q. Therefore, P. which may also be phrased as P → Q {\displaystyle P\rightarrow Q} (P implies Q) ∴ Q → P {\displaystyle \therefore Q\rightarrow...

analog of the above Poisson bracket of classical mechanics, the canonical commutation relation, [ X ^ , P ^ ] = X ^ P ^ − P ^ X ^ = i ℏ . {\displaystyle [{\hat...

{x}}} and p ^ {\displaystyle {\hat {p}}} that satisfy the canonical commutation relation [ x ^ , p ^ ] = i ℏ . {\displaystyle [{\hat {x}},{\hat {p}}]=i\hbar...

be (q,p), and let f be a function defined everywhere on phase space. In what follows, we fix operators P and Q satisfying the canonical commutation relations...

p_{n}^{k_{n}}q_{1}^{\ell _{1}}q_{2}^{\ell _{2}}\cdots q_{n}^{\ell _{n}}~,} with the commutation relations p k p ℓ = p ℓ p k , q k q ℓ = q ℓ q k , p k q ℓ − q ℓ p...

of the four. In addition, some models of TRIACs (three-quadrant high commutation triacs named by different suppliers as "logic level", "snubberless" or...

∇ p h j p − R p i j q h q p − R p i p q h j q = ∇ i ∇ j H − ( h p q h i j − h j p h i q ) h q p − ( h p q h i p − H h i q ) h j q = ∇ i ∇ j H − | h |...

elected by a mob intent on death." On April 22, 1915, an application for a commutation of Frank's death sentence was submitted to a three-person Prison Commission...

show that one could recover the Schrödinger equation or the canonical commutation relations from this rule. This was done by Feynman. Feynman showed that...

British Parliament passed legislation in 1825 that provided for the commutation of manorial land tenure, upon the agreement of the lord of the manor...

energy and time (unlike position q and momentum p, for example) do not satisfy a canonical commutation relation (such as [q, p] = i ħ). Various schemes have...

, q ] = 2 p × q , {\displaystyle [p,q]=2p\times q,} which gives the commutation relationship q p = p q − 2 p × q . {\displaystyle qp=pq-2p\times q.} In...

( p 2 , q 2 ) = ∑ P , Q ⊕ σ ( P , Q ) D ( P , Q )   , {\displaystyle D(p_{1},q_{1})\otimes D(p_{2},q_{2})=\sum _{P,Q}\oplus \sigma (P,Q)D(P,Q)~,} where...

fields obey canonical anticommutation relations rather than the canonical commutation relations of bosonic fields. The most prominent example of a fermionic...

unsuccessful military appeal, but filed a successful application for commutation of Manning's sentence in 2017. Hollander has been a partner at Freedman...

\ \left[\ Q,H\ \right]=0~.} Commutation implies that the eigenvalues (lower-case)   q   {\displaystyle \ q\ } are time-invariant:     d ⁡ q     d ⁡ t...

=\beta ,} for every 1-form β {\displaystyle \beta } on Q . {\displaystyle Q.} So, by the commutation between the pull-back and the exterior derivative, β...