In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative . There are different definitions used in group theory and ring theory.
What is a commutator abstract algebra?
In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.
What is commutator in maths?
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative . There are different definitions used in group theory and ring theory.
How do you solve a commutator?
The commutator [A,B] is by definition [A,B] = AB – BA . [A,BC] = B[A,C] + [A,B]C and [AB,C] = A[B,C] + [A,C]B. Proof: [A,BC] = ABC – BCA + (BAC – BAC) = ABC + B[A,C] – BAC = B[A,C] + [A,B]C.
What is the rule of commutator?
The commutator on the DC generator converts the AC into pulsating DC. ... On DC and most AC motors the purpose of the commutator is to insure that the current flowing through the rotor windings is always in the same direction , and the proper coil on the rotor is energized in respect to the field coils.
What does the commutator tell you?
A commutator in quantum mechanics tells us if we can measure two ‘observables’ at the same time. ... So the commutator tells us that observing the system in different orders effects the outcome . Going back to the Heisenberg example, taking a measurement of the position of a particle will disturb its momentum.
Is the commutator an operator?
Commutator. The Commutator of two operators A, B is the operator C = [A, B] such that C = AB − BA. If the operators A and B are scalar operators (such as the position operators) then AB = BA and the commutator is always zero.
What does a commutator do?
Note: In a generator, a commutator results in an output of direct current . In a motor, the commutator converts incoming alternating current into direct current before using it to generate motion.
Is slip ring a commutator?
Slip rings are used in AC motors to provide a continuous transfer of power whereas the commutators are used in DC motors to reverse the polarity of the current in the armature windings. ...
What is the anti commutator?
When talking about fermions (pauli-exclusion principle, grassman variables θ1θ2=−θ2θ1), the commutators have to be adjusted accordingly (change the minus sign) , thus become anti-commutators (in order to measure the same quantity).
How do you prove a Hermitian operator?
PROVE: The eigenfunctions of a Hermitian operator can be chosen to be orthogonal . Show that, if B F = s F & B G = t G & t is not equal to s, then <FG> = 0. PROVE: That in the case of degenerate eigenfunctions, we can construct from these eigenfunctions a new eigenfunction that will be orthogonal.
Is a Hermitian operator?
Hermitian operators are operators which satisfy the relation ∫ φ( ˆAψ)∗dτ = ∫ ψ∗( ˆAφ)dτ for any two well be- haved functions. Hermitian operators play an integral role in quantum mechanics due to two of their proper- ties. First, their eigenvalues are always real.
What is the difference between armature and commutator?
| Armature Commutator | It receives current from the armature windings It receives current from the armature core | The core consists of armature windings, commutator, and brushes It has some segments |
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How does a commutator convert AC to DC?
Commutator converts the Alternating to direct current in a DC generator . The alternating current generated in the armature windings of the generator gets converted to direct current after it passes through the commutator and the brushes.
What does it mean if commutator is zero?
A commutator in quantum mechanics tells us if we can measure two ‘observables ‘ at the same time. If the commutator of two ‘observables’ is zero, then they CAN be measured at the same time, otherwise there exists an uncertainty relation between the two.
