Commutation Definition and 220 Threads

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]...

Homework Statement Check that the spin matrices (Equations 4.145 and 4.147) obey the fundamental commutation relations for angular momentum, Equation 4.134.Homework Equations Eq. 4.147a --> S_{x} = \frac{\hbar}{2}\begin{pmatrix}0 & 1 \\ 1 & 0 \end{pmatrix} Eq. 4.147b --> S_{y} =...

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.

I have a problem with deriving another result. Sorry I am new to this field. Please see the attached PDF - everything is there.

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...

Does the usual commutation relations, e.g. between position and momentum, remains valid in relativistic quantum mechanics?

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...

sometimes I see [\hat{q},\hat{p}] = i\hbar\widehat{\{q,p\}} + O(\hbar^2) what does the last term O(\hbar^2) mean? x=y

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...

Does anyone know of any tables that show the commutation relations of all QM opeartors? Any information would be appreciated.