Relations Definition and 540 Threads

Hi there,... For a derivation of the Ehrenfestequations i found the following commutator relations for the Hamilton-Operator in a book: H = \frac{p_{op}^2}{2m} + V(r,t) and the momentum-operator p_{op} = - i \hbar \nabla respectively the position-operator r in position space: [H,p_{op}]...

[SOLVED] Viete relations problem Homework Statement Find all real numbers r for which there is at least one triple (x,y,z) of nonzero real numbers such that x^2 y + yz^2 + z^2 x = xy^2 + yz^2 + zx^2 = rxyzHomework Equations http://en.wikipedia.org/wiki/Vi%C3%A8te%27s_formulasThe Attempt at...

Hello, I was hoping someone could help point me in the right direction. I am trying to figure out how to solve recurrence relations using Mathematica (6). I have tried to search the web for information on how to use the recurrence relation solving package but I must be doing something wrong...

Homework Statement We are working on some problems for class and we are given statements which I accept as valid but don't know how to prove they are valid. I believe I have to utilize the maxwell relations but the terms seem unfamiliar to me.Homework Equations (1) Partial (d^2f / ds^2)_T = T /...

Homework Statement (proof) Determine whether or not (x,y)~(w,z) if and only if y=w is an equivalence relation. If it is, then describe the associated partition. Homework Equations The Attempt at a Solution Let x be an element of the reals. It is known that a relation on a set X...

Homework Statement A.) Jon wants to define a function f: A->B as invertible iff for all a in A and all b in B with f(a)=b, there exists a function g:B->A for which g(b)=a. Is that reasonable? B.) Determine Whether the relation ~ on the Real Numbers defined by x~y is reflexive, symmetric...

Relations question?!? Any help would be greatly appreciated! :confused:

[SOLVED] Recurrence Relations Homework Statement I need to express this recursive statement as a nonrecursive formula, using the technique of itteration. a_n = (n+1)a_{n-1} a_0 = 2 The Attempt at a Solution a_n = (n+1)a_{n-1} a_n = (n+1)(n+1)a_{n-2} = (n+1)^{2}a_{n-2} a_n =...

Hi all. Why Reynolds Analogy and other empirical relations always overesimate heat transfer? I have done an experiment on turbulent pipe flow (smooth pipe) and I used Reynold Analogy (both the simple (Pr=1) and the modified one) and the Dittus-Boetler correlation equation to do the...

Homework Statement Use the Maxwell relations and the Euler chain relation to express (ds/dt)p in terms of the heat capacity Cv = (du/dt)v. The expansion coefficient alpha = 1/v (dv/dt)p, and the isothermal compressibility Kt = -1/v (dV/dp)T. Hint. Assume that S= S(p,V) Homework Equations...

Given the Hamiltonian H = \vec{\alpha} \cdot \vec{p} c + \beta mc^2, How should one interpret the commutator [\vec{x}, H] which is supposedly related to the velocity of the Dirac particle? \vec{x} is a 3-vector whereas H is a vector so how do we commute them. Is some sort of tensor product in...

Homework Statement Let S be the set of integers. If a,b\in S, define aRb if ab\geq0. Is R an equivalence relation on S? Homework Equations The Attempt at a Solution Def: aRb=bRa \rightarrow ab=ba assume that aRb and bRc \Rightarrow aRc a=b and b=c since a=b, the substitute a...

Hi guys! The question is attached!...sorry!...theres weird symbols in the question any help would be v. much appreciated!:smile:

Hi guys I am having trouble with this question (i have attached). Any help with it would be very much appreciated. Many thanks in advance Pete

Hi :) I have my Discrete maths final in 2 days, and I was doing some practice questions and came across 2 parts that completely baffled me - I moved onto my course a bit late so I missed chunks from classes. please please please, can you explain them to me? I've put the questions in...

Homework Statement I came across a slightly unusual question today. It started out fine, just asking me to derive a maxwell relation but then asked under what conditions is this relationship valid. Homework Equations The Attempt at a Solution In deriving the relation I need to assume U...

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} =...

It's not often I'm shocked in a positive way, but could this be true? I forum where science "discussions" are at least consistantly of higher caliber then "evolution sukz because bible says so, lol"? I'm sorry if my shock confuses and annoys others on this board but imagine traveling through...

Given tanA=y/x.....(1) Can anyone tell me how you get the following relations: =>sinA=ay/sqrt(x^2+y^2).....(2) =>cosA=ax/sqrt(x^2+y^2)....(3) where a=(+/-)1 I know tanA=sinA/cosA and sin^2(A)+cos^2(A)=1...and I can see by substituting (2) and (3) into (1) it works, but I really...

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...

Are there any sets A for which (\mathcal{P}(A), \subseteq) is totally ordered? Prove your answer. To be courteous, I will include the definitions for partial ordering and total ordering. A relation is a partial order if the relation is reflexive, antisymmetric, and transitive. (in this...

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.

Alright, this is probably a really redundant question but for some reason it is giving me trouble. Let's say you are given the entropy of a black hole as: S=\frac{8\pi^2GM^2k}{hc} (thanks Stephen Hawking) And you have the relation between temperature and entropy/energy \frac{1}{T}=...

Hello all, I've been thinking about the connection between commutativity of operators and uncertainty. I've convinced myself that to have simultaneous eigenstates is a necessary and sufficient condition for two observeables to be measured simultaneously and accurately. It's also clear...

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

I am confused about completeness relations. I thought a completeness relation was something like: I = \sum_{i = 1}^n |i><i| = \sum_{i=1}^n P_i [ where P_i is the projection operator onto i. Now I saw this called a completeness relation as well: \delta(x - x') = \sum_{n=0}^\infty...

I know acoustic and optical phonons can interact with one another. Also, longitudinal and transverse phonons can interact with one another. I am wondering can a longitudinal phonon in one plane act with a transverse phonon from another plane to create a third phonon? Or, do these...

Homework Statement Explain why each of the following relations is not a functions for all reals. a. f\left( x \right) = \frac{1}{{x - 5}} b. f\left( x \right) = \frac{{1 + 2x}}{{1 + 5x}} c. f\left( x \right) = \sqrt {x + 2} how would i do this? and why is it so? many thanks...

I am trying to understand 3D Si dispersion relations and reciprocal lattice vectors. My confusion is that when I look at dispersion relations the wave vector typically is normalized from 0 to 1 by a/2pi. I thought the edge of the first BZ was pi/a. Is this correct or is it 2pi/a for a diamond...

Homework Statement A is some set. R is a relation (set of ordered pairs), and is transitive on A. S = {(x,y) | (x,y) is element of R, (y,x) is not element of R} Show that S is transitive and trichotomic on A. Homework Equations Transitivity: With xRy and yRz ==> xRz The...

Homework Statement Prove that if R is a symmetric relation on A, and Dom(R) = A, then R = the identity relation. 2. The attempt at a solution My problem is... I don't believe the claim. At all. If A = {1, 2, 3} and R = {(1, 2), (2, 1), (3, 1), (1, 3)}, that satisfies the antecedent, and...

Homework Statement Here's my problem - Give the order of linear homogeneous recurrence relations with constant coefficients for: An = 2na(n-1) The Attempt at a Solution I have no idea on how to start this problem - Any help would be greatly appreciated.

given that [x,p]=ih, show that if x=x, p has the representation p=-iħ∂/∂x+f(x) where f(x) is an arbitrary function of x

Homework Statement On the set of Natural Numbers from 1 to 10000 are given the following identity relations. R1 ; n R1 m where m and n have the same remainder by division by 24, that is mod n 24 == mod m 24. R2 ; n R2 m where n and m have in decimal notation the same number of 2s R3; n...

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...

Hello everyone. This problem has a few parts, and I'm on the last part and I'm having troubles and im' guessing my way is not the correct method. But here is the question. Let A be a set with 8 elements. a. how many binary relations are there on A? answer: A binary relation is any...

Homework Statement I need to express V in terms of Z and A. i know V= (3/5)Y + (2/5)Z given y=2A-3X X=(1/6)Z + (5/6)Y Homework Equations The Attempt at a Solution ok. my first attempt was to isolate y in the second equation, and let the two equations equal...

The cauchy Riemann relations can be written: \frac{\partial f}{\partial \bar{z}}=0 Is there an 'easy to see reason' why a function should not depend on the independent variable [itex]\bar{z}[/tex] to be differentiable?

I know that the functions e^{2 \pi inx} for n \in \mathbb{Z} are a base in the space of functions whith period 1. How do I derive the orthogonality relations for these functions?

I was wondering, what is the difference between an operator and a relation? For example, instead of saying 2+3 I can say Add(2,3). Or the \frac{df(x)}{dx} operator can be written as D(f(x)). I fail to see any difference between an operator and a relation. What do you guys think?

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

The Kramers-Kronig relations allows one to calculate the real part of the permitivity knowing the imaginary part or vice-versa: http://en.wikipedia.org/wiki/Kramers-Kronig_relations But in what situation will one know either the imginary part but not the real part or the real part but not the...

Is there a commonly-used name for a complete preorder (a transitive and total relation, Sloan's A000670 and A011782 for labeled and unlabeled, respectively) within set theory? (Not a total order, mind you -- it need not be antisymmetric.) I've heard the term "weak order", but that's from the...

-Let's suppose we have 2 gases ..one is a "Fermi" gas under an Harmonic potential and the other is a "Bose" gas under another Harmonic potential... in both cases (as an approximation) the particles (bosons and electrons are Non-interacting) then we could write the partition functions. \prod...

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...

Question: "Find a recurrence relation and initial conditions for the sequence {a sub n} if a sub n is the number of bit strings of length n that contain three consecutive 0's." So here's what I have so far... n > 3 n = 4, 1000, 0001 n = 5, 10000, 00001, 00010, 01000, 10001 n = 6...

Since we have anticommuting relations for the quantum Dirac fields, this will bring us to the similar classical correspondance but result in Grassmann spinor field function instead. (such as path integral) So when we consider an arbitrary interaction term that like (\bar{\psi} \psi)^n, if...

Okay, so I have a homework problem I'm a little confused about, The textbook is pretty useless and we didn't go into types of orders very much in class. So, am I to show that the dictionary order is reflexive, antisymmetric, and transitive on XxX, since XxX is already linearly ordered? I...

[SIZE="1"]Ok; this is another thread that covers two questions. I didn't want to mix them with my previous post; it's from the same 'section' but the questions are different. If any mods have issues with this, please say so. 1) If R \cup S is reflexive, then either R is reflexive or S is...

Ok so here's one of the questions we've been assigned... So I can graphically see what this relation looks like, and from that I've shown it's reflexive. Now I'm working on proving it as being symmetric, but I can't put it into words. b) ~ is symmetric. Well we want to show that aRb ->...