Commutation Definition and 220 Threads

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...

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...

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)] =...

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...

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...

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...

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...

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!

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...

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...

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...

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...

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...

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

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...

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} =...

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...

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.

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...

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...

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...

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...

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...

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 -...

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...

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}.

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

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

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"...

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.

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...

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...

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...

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...

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...

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?

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}...

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...

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...

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...

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...

what is the physical significance of the commutation of operators?

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...

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...

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...

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 ) ?

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=...

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...

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...

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...