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.
Hi, just wondering whether the commutation relation [\phi,L_3]=i\hbar holds and similar uncertainty relation such as involving X and Px can be derived ?
thanks
Homework Statement
Prove:
[σ⋅(p-qA)]²=(p-qA)²-q\bar{h}σ⋅B
where B=∇×A , p=i\bar{h}∇ and q is constant
Homework Equations
The Attempt at a Solution
if the x component is: px-qAx
and the y component is py-qAy
Then the x and y components shouldn't commute [px-qAx,py-qAy]...
In reviewing the derivation of the quantization of angular momentum-like operators from their commutation relations, I noticed that there is nothing a priori from which you can deduce the degeneracy of the eigenstates. While this is not a problem for angular momentum, in which other constraints...
Let the translation operator be:
F (\textbf {l} ) = exp \left( \frac{-i \textbf{p} \cdot \textbf{l}}{\hbar} \right)
where p is the momentum operator and l is some finite spatial displacement
I need to find [x_i , F (\textbf {l} )]
let me start with a fundamental commutation relation...
i need to find the commutation relation for:
[x_i , p_i ^n p_j^m p_k^l]
I could apply a test function g(x,y,z) to this and get:
=x_i p_i ^n p_j^m p_k^l g - p_i ^n p_j^m p_k^l x_i g
but from here I'm not sure where to go. any help would be appreciated.
what is it? i need to know everything about it. i know it encompasses a lot of different stuff but yea if someone could point me to a book or webpage that explains it thoroughly.
additionally what does this equal
\sigma_{\mu}\sigma_{\alpha}\sigma_{\alpha}\sigma_{\mu}
those are pauli...
Homework Statement
I need to show the commutation between the spin operator and a uniform magnetic field will produce the same result as the cross product between them.
Does this make sense? I don't see how it can be possible.
Homework Equations
[s,B]
(The s should also have a hat...
Is there a book that explain in a formal way the deduction of symmetry/antisymmetry of bosonic/fermionic wave equation e/o commutation relation? I've often noticed that some people use examples for the introcution, but is there an axiomatic deduction?
Homework Statement
I've just initiated a self-study on quantum mechanics and am in need of a little help.
The position and momentum operators do not commute. According to my book which attemps to demonstrate this property,
(1) \hat{p} \hat{x} \psi = \hat{p} x \psi = -i \hbar...
Homework Statement
The canonical commutation relations for a particl moving in 3D are
[\hat{x},\hat{p_{x}}]= i\hbar
[\hat{y},\hat{p_{y}}]= i\hbar
[\hat{z},\hat{p_{z}}]= i\hbar
and all other commutators involving x, px, y ,py, z , pz (they should all have a hat on eahc of them signifying...
I am working on a problem for homework and am supposed to show that the angular momentum operator squared commutes with H and that angular momentum and H also commute. This must be done in spherical coordinates and everything I see says "it's straightforward" but I don't see it. At least not...
I am reading the first chapter of Sakurai's Modern QM and from pages 30 and 32 respectively, I understand that
(i) If [A,B]=0, then they share the same set of eigenstates.
(ii) Conversely, if two operators have the same eigenstates, then they commute.
But we know that [L^2,L_z]=0...
Hi there, I need a help on one of the commutation proof,
the question is, show that [Lx,L^2]=0 cyclic where L=l1+l2
The expression simplifies to [Lx,l1l2]+[Lx,l2l1] but I'm not sure if they are 0.
Thanks for your help :D
I'm following a derivation (p85 of Symmetry Principles in Quantum Physics by Fonda & Ghirardi, for anyone who has it) in which the following assertion is made:
"...we have
\left[\mathcal{G}_p,\mathbf{r}_i\right] &=& \mathbf{v}_0t\mathcal{G}_p,
\left[\mathcal{G}_r,\mathbf{p}_i\right] &=&...
Hi, I have a question,
As it is said in QM, if two operators commute, they have so many common eigenstates that they form a basis. And the inverse is right.
Now there is the question,
if A,B,C are operators, [A,B]=0, [A,C]=0,
then is "[B,C]=0" also right?
If we simply say A and B, A and C...