What is Commutation: Definition and 220 Discussions

In law, a commutation is the substitution of a lesser penalty for that given after a conviction for a crime. The penalty can be lessened in severity, in duration, or both. Unlike most pardons by government and overturning by the court (a full overturning is equal to an acquittal), a commutation does not affect the status of a defendant's underlying criminal conviction.
Although the concept of commutation may be used to broadly describe the substitution of a lesser criminal penalty for the original sentence, some jurisdictions have historically used the term only for the substitution of a sentence of a different character than was originally imposed by the court. For example, the substitution of a sentence of parole for the original sentence of incarceration. A jurisdiction that uses that definition of commutation would use another term, such as a remission, to describe a reduction of a penalty that does not change its character.A commutation does not reverse a conviction and the recipient of a commutation remains guilty in accordance with the original conviction. For example, someone convicted of capital murder may have their sentence of death commuted to life imprisonment, a lessening of the punishment that does not affect the underlying criminal conviction, as may occur on a discretionary basis or following upon a change in the law or judicial ruling that limits or eliminates the death penalty.In some jurisdictions a commutation of sentence may be conditional, meaning that the convicted person may be required to abide by specified conditions or may lose the benefit of the commutation. The conditions must be lawful and reasonable, and will typically expire when the convicted completes any remaining portion of his or her sentence. For example, the pardon may be conditioned upon the person's being a law-abiding citizen, such that if the beneficiary of the commutation commits a new crime before the condition expires the original sentence may be restored.

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  1. A

    What is the significance of commutative operators in quantum mechanics?

    What do we mean by the two operators are commutative or non commutative? I wanted to understand the physical significance of the commutative property of the operators. We are doing the introduction to quantum mechanics and there are many things that are really confusing. Any help will be...
  2. E

    Engineering Two commutation processes for RL circuit

    Homework Statement I have to calculate first commutation process (t=0) and second commutation process (t1 = 2*τ) Both swithes are closing in the given time moment. Homework Equations Form of second commutation process: The Attempt at a Solution I have already calculated...
  3. H

    Beam Splitter - Commutation relations

    Hi guys, why does the following mean B is unitary? if we have two rotations such that; b1 = B11a1 + B12a2 b2 = B21a1 + B22a2 and the following commutator results are; [b1, b1(dagger)] = |B11|^2 + |B12|^2 --> 1 [b2, b2(dagger)] = |B21|^2 + |B22|^2 --> 1 [b1, b2(dagger)] =...
  4. C

    Lie dragging preserves commutation proof.

    Hi! A proof of Frobenius' theorem (in Schutz Geometrical Methods) uses the fact that if a set of vector fields ##{V_{(a)}}## commute on some submanifold S of an ambient manifold M, and one use an additional vector field ##Z## to Lie transport/drag the set ##{V_{(a)}}## around the manifold M...
  5. E

    Engineering Two commutation processes for RL circuit.

    Homework Statement I have to calculate first commutation process (t=0) and second commutation process (t = 2*τ) Both swithes are closing in the given time moment as I wrote before. Homework Equations The Attempt at a Solution I'll do this task step by step, that's why here...
  6. M

    Dirac Notation and commutation

    Hi everyone, my problem is this Using Dirac notation show that \frac{d}{dt}<\varphi|\hat{A}|\varphi> = \frac{i}{\hbar}<\varphi|[\hat{H},\hat{A}]|\varphi> where A does not explicitly depend on t I am given as a hint that the hamiltonian operator in Dirac notation is...
  7. C

    Commutation relations between P and L

    Homework Statement Compute the commutation relations of the momentum operator ##\underline{\hat{P}}## and the angular momentum operator ##\underline{\hat{L}}## Homework Equations $$\hat{L_i} = -i\hbar \epsilon_{ijk} x_j \frac{\partial}{\partial_k} = \epsilon_{ijk}x_j \hat{P_k}$$ The...
  8. D

    Pauli matrices and the Levi-Civita tensor : commutation relations

    Homework Statement Whats up guys! I've got this question typed up in Word cos I reckon its faster: http://imageshack.com/a/img5/2286/br30.jpg Homework Equations I don't know of any The Attempt at a Solution I don't know where to start! can u guys help me out please? Thanks!
  9. S

    Forced Commutation Clarrification

    Hey all, I am merely looking for clarrification as to what happens with the circuit that I have provided an image of. Please assume all elements are ideal (for simplicity). I come here for assurance as I cannot seem to find it anywhere else. Thanks in advance! Thyristor T1 is fired at...
  10. T

    Directional Derivatives and Commutation

    Homework Statement I need to prove that directional derivatives do not commute. Homework Equations Thus, I need to show that: (\vec{A} \cdot \nabla)(\vec{B} \cdot \nabla f) - (\vec{B} \cdot \nabla)(\vec{A} \cdot \nabla f) = (\vec{A} \cdot \nabla \vec{B} - \vec{B} \cdot \nabla...
  11. G

    Commutation relation of the creation/annihilation operators in a field

    Hello, I'm having trouble calculating this commutator, at the moment I've got: \left[a_{p},a_{q}^{\dagger}\right]=\left[\frac{i}{\sqrt{2\omega_{p}}}\Pi(p)+\sqrt{\frac{w_p}{2}}\Phi(p),\frac{-i}{\sqrt{2\omega_{p}}}\Pi(p)+\sqrt{\frac{w_p}{2}}\Phi(p)\right]=i\left[\Pi(p),\Phi(q)\right]=i\int...
  12. C

    Spherical tensor operators' commutation with lowering/raising operator

    I'm studying Shankar's book (2nd edition), and I came across his equation (15.3.11) about spherical tensor operators: [J_\pm, T_k^q]=\pm \hbar\sqrt{(k\mp q)(k\pm q+1)}T_k^{q\pm 1} I tried to derive this using his hint from Ex 15.3.2, but the result I got doesn't have the overall \pm sign on the...
  13. P

    Verify the commutation relations for x and p by definition.

    Homework Statement Verify ##\left[ x^{i} , p_{k}\right] = i \hbar \delta^{i}_{k}## Homework Equations ## p_{j} = -i \hbar \partial_{j}## The Attempt at a Solution Writing it out i get $$ i \hbar \left( \partial_{k} x^{j} - x^{j} \partial_{k} \right)$$ The Kronecker makes perfect sense, it's...
  14. R

    What is ↔ mean? in commutation relation?

    I found this in Srednicki's QFTbook. I don't know what ↔ means. Help me, please
  15. tomwilliam2

    Checking a commutation relation for angular momentum and lin. momentum

    Homework Statement Prove the commutation relation ##\left [L_x, p_y \right] = i\hbar \epsilon_{xyz} p_z## Homework Equations ##L_x = yp_z - zp_y## ##p_z = i\hbar \frac{\partial}{\partial z}##The Attempt at a Solution ##\left [L_x, p_y \right] = (yp_z - zp_y)p_y - p_y(yp_z - zp_y)## ##\left...
  16. D

    Behaviour of an Exponential Commutation

    Homework Statement Forgive the awkward title, it was hard to think how to describe the problem in such a short space. I'm following the proof of Proposition 1.2 of Nakahara's "Geometry, Topology and Physics", and the following commutation relation has been established: \partial_x^n e^{ikx} =...
  17. S

    Total Angular Momentum Commutation Relations for 2 Particle

    Hey, I'm not exactly sure how much this question wants, however the two in question are parts a) and b) below. So part a) asks to write the expression for the total angular momentum J, I though this was just: \hat{J}=\hat{J}^{(1)}+\hat{J}^{(2)} but when we come to showing it...
  18. A

    The Role of Commutators and Poisson Brackets in Phase Space Geometry

    Should I in any way find this intuitive? Apart from the fact that the idea of a commutation relation resembles the idea of a poisson bracket for operators I can't see how I should find it intuitive.
  19. R

    Operators Commutation: Explaining P(x), L(y)

    Can someone please explain to me how do we get the following: [P(x), L(y)]= i h(cut) P(z) P(x) is the momentum operator with respect to x and L(y) is the angular momentum operator with respect to y. I have also attached the solution. I am stuck at the underlined part. I do not know how...
  20. C

    Commutation Relationships and Operator Functions

    There are 2 operators such that [A,B] = 0. Does [F(A),B]=0 ? Specifically, let's say we had the Hamiltonian of a 3-D oscillator H and L^2. We know that L^2 = Lx^2+Ly^2+Lz^2, and it is known that [H,Lz] = 0. Can we say that since H and Lz commute, H and Lz^2 also commute, by symmetry H and...
  21. J

    Determining the commutation relation of operators - Einstein summation notation

    Determining the commutation relation of operators -- Einstein summation notation Homework Statement Determine the commutator [L_i, C_j] . Homework Equations L_i = \epsilon_{ijk}r_j p_k C_i = \epsilon_{ijk}A_j B_k [L_i, A_j] = i \hbar \epsilon_{ijk} A_k [L_i, B_j] = i \hbar...
  22. P

    Bitensor covariant derivative commutation

    Hi everyone, I'm trying to prove a relation in which I need do commute covariant derivatives of a bitensor. The equation is quite long but I need to write something like this: Given a bitensor G^{\alpha}_{\beta'}(x,x'), where the unprimed indexes (\alpha,\beta, etc) are assigned to the...
  23. P

    Covariant Derivative Commutation

    Hello, Can anyone tell me the general formula for commuting covariant derivatives, I mean, given a (r,s)-tensor field what is the formula to commute covariant derivatives? I found a formula http://pt.scribd.com/doc/25834757/21/Commuting-covariant-derivatives page 25, Eq.6.18 but it doesn't...
  24. M

    Generator of Rotations and commutation relationships

    Suppose we have [J_i,J_j] = \sum_k \epsilon_{ijk} J_k and [L_i,L_j] = \sum_k \epsilon_{ijk} L_k 1st question, I am right in thinking that J represents Eingavalues for spin 1/2 particles... next... Computing the commutation relations, I find that \sum_k \epsilon_{ijk} (J_K + L_K - L_k -...
  25. mnb96

    Can Commutation between Subgroups be Achieved without Assuming Normality?

    Hello, let's suppose I have two subgroups R and T, and I know that in general they do not commute: that is, rt\neq tr for some r\in R, t\in T. Is it possible, perhaps after making specific assumptions on R and T, to find some r'\in R, and t'\in T such that: rt=t'r'. This is possible, for...
  26. M

    Commutation of differential operators

    Homework Statement Evaluate the commutator \left[\frac{d}{dx},x\right] Homework Equations \left[A,B\right]=AB-BA The Attempt at a Solution \left[\frac{d}{dx},x\right]=1-x\frac{d}{dx} I don't know how to figure out x\frac{d}{dx}.
  27. S

    Significance of commutation of operators? position and momentum

    significance of commutation of operators? how do u show that the position and momentum operators do not commute?
  28. S

    Operators and commutation of operators

    why is only one component of angular momentum is quantised, and what determines which component is quantised?
  29. shahbaznihal

    Covariant commutation relation in Mandl and Shaw

    Hi, I am trying to study Quantum Field Theory by myself from Mandl and Shaw second edition and I am having trouble understanding the section on covariant commutation relations. I understand the idea that field at equal times at two different points commute because they cannot "communicate"...
  30. S

    Is the delta in the commutation relations of QFT a dirac delta or a kronecker?

    If it's a dirac delta doesn't it mean it's infinite when x=y? Or is it a sort of kronecker where it's equal to one but the indices x and y are continuous? I'm confused.
  31. E

    Transition from Poisson bracket into Canonical Commutation Relations

    In book http://www.phy.uct.ac.za/people/horowitz/Teaching/lecturenotes.pdf in section 2 it is described transition from Poisson bracket into Canonical Commutation Relations. But it is written The experimentally observed phenomenon of incompatible measurements suggests that position and...
  32. B

    Quantum and Commutation - Help me start

    Homework Statement http://www.bravus.com/question.jpg Homework Equations See below The Attempt at a Solution Below are my scribbles toward a solution. The point is that the two expressions are different *unless* either the operators A and B or the operators B and C commute...
  33. K

    Engineering Commutation process in RLC circuit

    Homework Statement Still can't figure this one out. All data is on the picture attached. I have to find the current flowing through E1 after E2 is connected and draw a graph as it changes in time of the process. I can't do the equations when t=0 Homework Equations dUc/dt|t=0...
  34. S

    Commutation relations for Spin opertors

    Dear physicist, I designed an experiment for my undergraduate students. As we know, for spin operators, the commutation relation is [Si,Sj]=ihSk We also know, if we use two polarizers which are perpendicular each other, there is no light other side after polarizers. Namely apparatus is...
  35. O

    Relation between commutation and quantization

    relation between "commutation" and "quantization" Hi people; Over the several texts I have read, I got the impression that position-momentum commutation relations is the cause of "quantization" of the system. Or, they are somehow fundamentally related. The only relation I know of, is to...
  36. H

    Can changes in spring constant affect the eigenstates of a harmonic oscillator?

    We now that if [A,B]=0, they have the same eigenstates. But consider a harmonic oscillator with the spring constant k1. If we change k1 to k2, then [H1,H2]=0 and the above expression implies that the eigenstates should not change while they really change! Could you please tell me if i am wrong?
  37. F

    Pauli-Lubanski pseudovector commutation relations

    Homework Statement Hi. This is not a homework question per se, but more of a personal question, but I thought I'd post it here. I'm trying to prove the commutation relations of the Pauli-Lubanski pseudovector \begin{equation} W_\mu\equiv-\frac{1}{2}...
  38. J

    Observables and Commutation (newbie questions?)

    Some questions. Am I getting this basically right? What does a "state vector" look like? It looks like |α> or |β> But more than that... It is a complex vector in Hilbert space? Now, you get "observables" from state-vectors by performing operators on them. So the state-vector...
  39. A

    Operators satisfying abstract commutation relation; then finding an eigenvalue.

    So, my problem statement is: Suppose that two operators P and Q satisfy the commutation relation [Q,P] = Q . Suppose that ψ is an eigenfunction of the operator P with eigenvalue p. Show that Qψ is also an eigenfunction of P, and find its eigenvalue. This shouldn't be too difficult, but...
  40. X

    Quantum Mechanics: Uncertainty and Commutation relation

    I am stuck on one part of my Quantum Mechanics HW. Above the question it says "Try and answer the following question." So I can only assume that he isn't looking for something incredibly detailed. (Ill explain why after the question is given.) Homework Statement What is the meaning of the...
  41. D

    Commutation property of covariant derivative

    My book defines the covariant derivative of a tangent vector field as the directional derivative of each component, and then we subtract out the normal component to the surface. I am a little confused about proving some properties. One of them states: If x(u, v) is an orthogonal patch, x_u...
  42. S

    Understanding the Physical Significance of Operator Commutation

    what is the physical significance of the commutation of operators?
  43. B

    Commutation relations of angular momentum with position, momentum.

    Homework Statement Using the position space representation, prove that: \left[L_i, x_j\right] = i\hbar\epsilon_{ijk}x_k . Similarly for \left[L_i, p_j\right] . Homework Equations Presumably, L_i = \epsilon_{ijk}x_jp_k . \left[x_i, p_j\right] = i\hbar\delta_{ij} . The Attempt at a...
  44. K

    Commutation of Curl and the partial time derivative?

    I am curious if there are any issue with commuting the curl of a vector with the partial time derivative? For example if we take Faraday's law: Curl(E)-dB/dt=0 And I take the curl of both sides: Curl(Curl(E))-Curl(dB/dt)=0 Is Curl(dB/dt)=d/dt(Curl(B)) I assume this is only...
  45. B

    Show that the operators J(+)-hat and J(-)-hat satisfy the following commutation

    Homework Statement The operators J(subscript x)-hat, J(subscript y)-hat and J(subscript z)-hat are Cartesian components of the angular momentum operator obeying the usual commutation relations ([J(subscript x)-hat, J(subscript y)-hat]=i h-bar J(subscript z) etc). Use these commutation...
  46. B

    Commutation of Hamiltonian and time evolution operator

    Can anyone explain how the time evolution operator commutes with the Hamiltonian of a system ( given that the the Hamiltonian does not depend explicitly on t ) ?
  47. A

    Commutation of Angular and Linear Momentum

    If I have a relation such as [L_{j} , \vec{p}^2]=0 where j=x,y,z. Can I re-write it as [L_{j}, \vec{p} \vec{p}]=0 and then evaluate it as though it were an identity? e.g. [A,BC]=[A,B]C+[B,A]C=...
  48. K

    Commutation relation of operators involving momentum and position

    Homework Statement The problem is number 11, the problem statement would be in the first picture in the spoiler. Basically, I'm trying to find if two operators commute. They're not supposed to, since they involve momentum and position, but my work has been suggesting otherwise, so I'm doing...
  49. J

    Canonical Commutation Relations: Why?

    Virtually every treatment of quantum mechanics brings up the canonical commutation relations (CCR); they go over what the Poisson bracket is and how it relates to a phase space / Hamiltonian mechanics, and then say "then, you replace that with ih times the commutator, and replace the dynamical...
  50. 0

    A paradox in commutation relation

    The following paradox was put forward by "Fredrik" in a discussion on "time-uncertainity relation"- Lets look at this closely, using position momentum operators and a general quantum state- \langle U|xp - px|U \rangle This can be rewritten as- \sum_{x'}\sum_{x"}\sum_{p'} (\langle...
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