Bracket Definition and 79 Threads

Hello, why is <j' m' | j m>=0 if j \not= j' \; \text{or} \; m \not= m' j and m are describing states. I don't understand why an 'empty bracket' behaves like that.

Homework Statement Show that if the vector fields X and Y are linear combinations (not necessarily with constant coefficients) of m vector fields that all commute with one another, then the lie bracket of X and Y is a linear combination of the same m vector fields. The Attempt at a Solution...

I have searched in web and go through some papers. But the use of Dirac Bracket in constraint still unclear to me. It would be better if I have some examples. Can anyone please help me by suggesting books/references where I can find details about using Dirac Bracket?

hello! My first post here. I am by no means a mechanical engineer as I studied computer science in college. My question has to do with adding what is known as a cold air intake onto my vehicle. The design of the intake is such that the pipe fits at the throttle body via a silicone/rubber...

How is everyone's bracket looking. Right now I'm in the 85th percentile for espn and I'm happy with that. Final Four: Syracuse over Duke Kansas over Wisconsin Championship: Syracuse over Kansas I don't actually think Syracuse will win but to win pools with tons of people it is smart...

I'm having difficulties in finding an answer to the issue show in the attached pic. Fracture surface on the failed bracket! I have the properties of the mild steel, the properties of the rubber mountings, and the number of the cycles per minute. What i can't figure out is the load or the force...

Hi all, I am trying to calculate a value for stress in a right angled bracket. this would be simple for me if the load was a static load, it would cause the bracket to bend around a point etc so i can get moments to find its bending stress. however this bracket will be stopping a moving...

So, I am learning about tangent-valued differential forms, operations on forms and Frolicher-Nijenhuis bracket, and I am writing a blog about what I have learned. In two monographs I have spotted a formula that - as far as can see - has a missing factor. At least this is how I understand what...

I am designing these brackets on a ventilation system to hold filters that my company stocks regularly. The vent is about 49.5"x49.5" and the filters are about 23.5"x23.5". Placing 4 filters in this square vent leaves about 1.25" on each side. I have designed the brackets so that they block the...

Homework Statement A T-shaped bracket supports a 150-N load as shown. Determine the reactions at A and C when (a) \alpha=90o, (b) \alpha=45o ans: (a)A=150N going down, C=167.7N,63.4degrees (b)A= 194.5N going down; C=253N, 77.9degrees base on the book...

My questions are: - Will a proposed bracket be able to support 7500 lb. without undue or permanent distortion or failure? - Can the proposed dimensions be improved? The bracket will be attached to a large tree and will support one end of the 4x6 redwood swingset beam. (On the other end...

I need a hand choosing the right size, thickness and shape of steel for a bracket to mount an old style 5 gallon Jerry water can on a Jeep. I estimate the weight of the can + water + misc = 50 to 55 pounds. The bracket will be subjected to rough off-road conditions. In the drawing the red...

How can I work out {π,∂φ} where {,} is a Poisson Bracket; π is the canonical momentum and ∂φ is the spatial derivative of the field (ie. not including the temporal one). Basically the question boils down to (or atleast I think it does!), working out ∂(∂φ) /∂φ - ie. differentiating the...

If we have vect (u) which denotes an infinite-dimensional vector space of all vector fields on u. As infinitesimal elements of the continuous group of Diff(u) they form a Lie Algebra. We then can define the bracket of two vector fields in v and w. If in coordinates: v = \sum_{i}V i...

Hi! I was doing an assignment in quantum mechanics and came upon the following fact I cannot explain to me. I hope someone of you can and will be willing to :) Consider the creation and annihilation operators: a^+ and a and also the momentum and position operators p and x...

Homework Statement A 10kg block is resting on a 5kg bracket, which rests on a frictionless surface. The coef. of static and kinetic friction between the block and bracket are .4 and .3, respectively. Find out a) the max force that can be applied to the block without the block sliding on the...

Hello, I'm just unsure about the use of curly brackets in expressing loci of complex number z, to which I've been introduced in our calculus class: - I can't find elaborations on this on-line :confused: - No material I can find in our textbooks(?) I do know it is used to express the...

i've never really done a proof by induction but i would like to prove a statement about commutator relations so can you please check my proof: claim: [A,B^n]=nB^{n-1}[A,B] if [A,B]=k\cdot I where A,B are operators, I is the identity and k is any scalar. proof: [A,B^2] = [A,B]B+B[A,B] =...

I'm installing a set of front brake calipers on my track car, and the mounting brackets are made of aluminum (7075). What is the better mounting scenario - Thread the mounting bolts directly into the aluminum, or use a through hole mounting method with a proper bolt and nut combination? The...

I have a Samsung 42" similar to this one: http://www.hotchickshotpicks.com/wp-content/uploads/2007/09/samsung-42-inch-tv.jpg except that of course mine doesn't show sports. I've mounted it on a wall support but the TV does not seem stable. I can grab it and wobble it. The wall support is...

Hi Guys I hope you can help. I’m currently trying to modify some existing equipment and have a problem that I hope you good people can help me solve. I have a fabricated bracket that currently supports another bracket than runs on linear bearings to position its self. see attached JPG for...

When asked to find the domain, what bracket is used to denote that a number is excluded or included in the domain, ( or [?

We have to show that [Lx,Ly] = Lz [Ly,Lx] = -Lz [Lx,Lx] = 0 and I have done this. We then need to comment on the significance of these results, which I'm not sure of. I know in QM you get similar results for commutators of these quantities, and it means that you can't simultaneously know...

If you have the metric g_{ab} , \pi _{ab} as the metric and "generalized momenta", my question is if you can define GR using Poisson Bracet: \dot g_{ab} =[g_{ab},H] \dot \pi _{ab}=[\pi _{ab},H] and hence use these equations to obtain and solve the metric.:shy:

A shelf bracket is mounted on a vertical wall by a single screw, as shown in Figure P12.59. Neglecting the weight of the bracket, find the horizontal component of the force that the screw exerts on the bracket when an F = 86.0 N vertical force is applied as shown. Ok so we have three...

Hi everyone, This is my first post here :smile: Anyway I have problems solving this question wonder anyone could help give me some clues as to how to go about it. Here goes: The positive integers are bracketed as follows, (1), (2,3), (4,5,6,7), (8,9,10,11,12,13,14,15), ...

Dear all, Please help me to solve the following problems about Poisson brackets. Let M be a 2n-manifold and w is a closed non-degenerate di®eren- tial 2-form. (Locally we write w = w_ij dx^i ^ dx^j with [w_ij ] being a non-degenerate anti-symmetric real matrix-valued local function on M)...

From this reference: titled From Classical to Quantum Mechanics, I quote the following: ( \xi^i are coordinate functions) Let M be a manifold of dimension n. If we consider a non-degenerate Poisson bracket, i.e. such that \{\xi^i,\xi^j\} \equiv \omega^i^j is an inversible...

one elementary result that you see when you first learn differential geometry is that the pushforward of the Lie bracket of two vector fields is the Lie bracket of the pushforward of the two vector fields, i.e. let \phi be a diffeomorphism from manifold M to N, and let v, w be two vector...