Relation Definition and 1000 Threads

Hello. I'm having trouble understanding what is required in the following problem: Find the relation between the matrix elements of the operators $\widehat{p}$ and $\widehat{x}$ in the base of eigenvectors of the Hamiltonian for one particle, that is, $$\widehat{H} = \frac{1}{2M} \widehat{p}^2...

With the increase in RPM could the electric out put of a generator be increased.

I need a equation relating no. of turns of primary+ secondary, temperature increased due to eddy currents.

Is this equation of any use or in any way interesting? c = speed of light (m/s) e = euler's number I don't know much about physics but 2^6=log_2(64), this is a binary logarithm so would this mean that computers, the world (c and e) and circles(pi) all be related somehow by this equation?

I have a problem. As I was finding the torque for an engine. I have. I get a question about the relation of acceleration and time. How will be the graph of varying acceleration and time if acceleration decreases? Will it be a straight line with negative slope or any other shape?

Hi, If f'(x) >= f'(y) can we say that f''(x) >= f''(y) also holds ? And if yes under which conditions ? Thanks

What is the relation between classical from quantum vs measurement problem. On one hand they seem to be related on the other they seem to be of different nature. We always see our screens on front of us and not 100 meters away, that we say is classical object although the screen is a quantum...

Homework Statement I need to calculate the energy dispersion relation in the tight binding for simple cubic, base centered cubic and face centered cubic crystals. There are no values given, they just need the result depending on the lattice constant a. Homework Equations E (k) = alpha + beta *...

Hi, I was wondering if anyone here could help me prove or disprove this empirical observation or explain why there seems to be a connection between automorphic generators described below and the automorphisms of these groups: Consider the p-group expansion: ##\mathbb{Z}_n^*\cong S_2\times...

Homework Statement To show [J2, J+] = 0 2. Homework Equations J+ = Jx + i Jy [J2, Jx ] = 0 [J2, Jy ] = 0The Attempt at a Solution Step 1: L.H.S. = [J2, J+] Step 2: L.H.S. = [J2, Jx + i Jy ] Step 3: L.H.S. = [J2, Jx ] + i [J2, Jy ] Step 4: L.H.S. = 0 + 0 Step...

Hi! (Wave) I want to show that the Euler equation for the functional $J(y)= \int_a^b f(x,y) \sqrt{1+y'^2}dx$ has the form: $$f_y-f_xy'-\frac{fy''}{1+y'^2}=0$$$$L(x,y,y')= f(x,y) \sqrt{1+y'^2} dx$$ Substituting $L_y(x,y,y')=f_y(x,y) \sqrt{1+y'^2}, \ L_{y'}(x,y,y')= f(x,y)...

Hello. I am trying to wrap my head around where from did he got the x = sin of theta equation at the 32:44 mark of the video: . Isn't sine of theta x over the hypotenuse in the diagram ? Thanks in advance!

In class I learn that we can get the dispersion relation for particles by using E=hbar*w and p=hbar*k. The calculated phase velocity is w/k = hbar*k/2m, while the group velocity is dw/dk=hbar*k/m. All these make sense to me, except one thing: I always thought that E=hbar*w=hf is only applicable...

Hi, I have a question about how to find the particular solutions when trying to solve recurrence relations. For example, trying to solve an+2 = -4an + 8n2n , I begin with finding the roots in the characteristic polynomial associated with the homogeneous equation, so r1 = 2i and r2 = -2i...

Hi. Here's the dispersion relation for a diatomic linear chain, where the distance is a/2 between each atom. My issue here is that if you set m_1=m_2=m, i.e. set both atoms equal to each other, it doesn't automatically reduce to the old acoustic dispersion relation as the ± term doesn't...

Hi Friends! Please tell me if the question below is valid? "If the frequency of the source is changed from f to 2f ,keeping amplitude same,then total energy is changed by what amount?" What I conclude is"We can think it in two ways: 1 In classical sense,where I could not find any...

Homework Statement If matrix ## C = \left[ {\begin{array}{c} A \\ B \ \end{array} } \right]## then how is N(C), the nullspace of C, related to N(A) and N(B)? Homework Equations Ax = 0; x = N(A) The Attempt at a Solution First, I thought that the relation between A and B with C is ## C = A...

Homework Statement If S2 = at2+ 2bt+c, then the acceleration is A) Directly proportional to S B) Inversely proportional to S C) Directly proportional to S2 D) inversely proportional to S3 Homework Equations dS/dt = v dv/dt = A The Attempt at a Solution Differentiating both sides, 2Sv = 2at +...

Homework Statement Given an NxN symetric tri-diagonal matrix, derive the recursion relation for the characteristic polynomial Pn(λ) Homework Equations Pn(λ) = |A -λI | Pn(λ) = (An,n - λ)Pn-1(λ) - A2n,n-1Pn-2(λ) The Attempt at a Solution This was easy to do by induction, but I am always...

Regarding interacting green's function, I found two different description: 1. usually in QFT: <\Omega|T\{ABC\}|\Omega>=\lim\limits_{T \to \infty(1-i\epsilon)}\frac{<0|T\{A_IB_I U(-T,T)\}|0>}{<0|T\{U(-T,T)\}|0>} 2. usually in quantum many body systems...

Hello guys, I'm currently working on a car simulation just for fun, but I'm stuck... The force to move a car is generated by burning fuel ( to be more percise, diesel or gasolin). But there are more variables: Pressure (i know this because of turbos and such) amount of fuel amount of air (or...

how can we relate innermost stable circular orbits, keplerian, epicyclic, frame dragging precession frequency with dipole moment.

Homework Statement We know about the equation: ##Fe+2HCl(g) \longrightarrow FeCl_2+H_2##. In my textbook it's written that liberation of ##H_2## prevents formation of ##FeCl_3##. But why?And how?Homework EquationsThe Attempt at a Solution I think it is related to the Le-Chatelier principle . As...

Homework Statement If a,b,c,d ∈R+ and a,b,c,d are in H.P. Then 1. a+ d > b+ c 2. a+ c > b+ d 3. a + b > c+d 4. a-b > c-d Homework Equations Don't know which equation to apply The Attempt at a Solution 1/a, 1/b , 1/c and 1/d would be in A. P 1/b -1/a = 1/d - 1/c

The closure relation in infinite dimension is : ∫|x><x|dx =I (identity operator),but if we apply the limit definition of the integral the result is not logic or intuitive. The limit definition of the integral is a∫b f(x)dx=lim(n-->∞) [i=1]∑[i=∞]f(ci)Δxi, where Δxi=(b-a)/n (n--.>∞) and...

Recall that the Fibonacci sequence is defined by the initial conditions F0 = 0 and F1 = 1, and the recurrence relation Fn = Fn−1 + Fn−2 for n > 2. (a) Let F(z) = F0 + F1z + F2z 2 + F3z 3 + · · · be the generating function of the Fibonacci numbers. Derive a closed formula for F(z). (b) Consider...

Homework Statement hello all, I'm in the middle of solving a d.e using the series method. I have come across a weird pattern in part of my solution that I'm confused about: 6, (6)(10),(6)(10)(14),(6)(10)(14)(18),... Homework EquationsThe Attempt at a Solution I can see its 2(3), 2(3)*2(5)...

Why flowing current in wire creat magnetic field...if anybody say this is because of spin quantum number,... So i just want to say spin quantum number is because of wave nature of electron.i just want to know what effect of dual nature of electron on magnetic field.:rolleyes:

1. (16+x2)-xy'+32y=0 Seek a power series solution for the given differential equation about the given point x0 find the recurrence relation. So I used y=∑Anxn , found y' and y'' then I substituted it into the original equation, distributed, made all x to the n power equal to xn, made the...

Hi guys, first ever post. My question is if light travels at the same speed regardless of its wavelength, doesn't this statement seem to contradict itself? If the light simply traveled in a straight line then sure, but different wavelengths i would think mean that a greater distance would...

I am trying to conceptually connect the two formulations of quantum mechanics. The phase space formulation deals with quasi-probability distributions on the phase space and the path integral formulation usually deals with a sum-over-paths in the configuration space. I see how they both lead...

Homework Statement It is given in my book that: ΔStotal=ΔSsystem+ΔSsurrounding Where S is entropy. ΔSsurr=-ΔH/T Therefore: ΔStotal=ΔSsystem+[-ΔHsystem/T] As we can see here that ΔSsurrounding=-ΔHsystem/T is applied here . But is this relation correct? Homework Equations ΔS=qreversible/T Where...

Homework Statement for functions f: X -> Y and g: Y ->Z show that for all subsets C in Z , (g°f)^-1(C) ⊆ f^-1(g^-1(C)) (or find a counterexample) The Attempt at a Solution let z ∈ (g°f)^-1(C) such that (g°f)^-1(z) = x for some x∈X then z = (g°f)(x) z = g(f(x)) g^-1(z) = f(x) f^-1(g^-1(z) = x...

I'm trying to get my head around what this means exactly. I've plotted the graph to help verse me with the functions that I've derived. From the free electron model, the wavefunctions are treated as planewaves of the form \psi_\mathbf{k}(\mathbf{r}) = e^{i\mathbf{k}\cdot\mathbf{r}} Due to...

I am very confused about concepts of energy and work. I try to understand this way: there are many kinds of energy. every force is related with one kind of energy,but there is special one,the kinetic energy relate with the "sum force"

Homework Statement Give the equivalence classes of the relation aRb if and only if a^4 ≡ b^4 (mod 30) on the set {1, 2, 3, . . . , 15}. Homework Equations Definition of modular arithmetic. Definition of equivalence class. The Attempt at a Solution I can successfully do this problem using...

Hey all, I’ve scoured the internet in search of an answer to no avail, so it’s time to ask the experts!My background is more Chemistry and Biology, not Physics, or specifically fluid dynamics, so bear with me! Also, this is a little long, so I will do my best to make it easy to follow.The...

If H(x)= \int_c^x h(x)dx and H(a) = F(a) - G(a) = \int_c^a h(x)dx and H(b) = F(b) - G(b) = \int_c^b h(x)dx, then does that mean H(x) = F(x) - G(x)? Is the information provided sufficient enough to come to that conclusion?

Hey! :o How can we prove by induction the relation $A(x,y)>y, \forall x,y$ ?? (Wondering) When we have to prove a relation $P(n), n\geq 0$, we do the following steps: we show that it stands for $n=0$ we assume that it stands for n=k (Induction hypothesis) we want to shw that it...

Homework Statement If a relation R on N × N is (a,b)R(c,d) iff ad(b+c) = bc(a+d) Homework Equations -- The Attempt at a Solution I got the reflexive and symmetric parts but not the transitive part... here's what i have ## (a,b)(c,d)∈R and (c,d)(e,f)∈R## To prove ##(a,b)(e,f) ∈ R## .i.e...

Would this example be valid in satisfying a relation that is symmetric and anti-symmetric? The relation R = {(1,1),(2,2)} on the set A = {1,2,3} Also, I'm curious to know since relations can both be neither symmetric and anti-symmetric, would R = {(1,2),(2,1),(2,3)} be an example of such a...

Looking at an exposition of Kripke semantics, the relationship ||- in a Kripke model is obviously supposed to be similar to the model relation |= . A possible world (a node) looks suspiciously like a model for second-order formulas. But of course it cannot be this simple. What is the connection...

Given the image: http://i.stack.imgur.com/EJ3ax.jpgand that $x_0 = 1, y_0=0$ and $\text{angles} \space θ_i , i = 1, 2, 3, · · ·$ can be arbitrarily picked. How can I derive a recurrence relationship for $x_{n+1}$ and $x_n$? I actually know what the relationship is, however, don't know how to...

Homework Statement prove that s_k <= 2s_{k-2}+3 for all ints k >= 3 if s1=1 and s2 = 3 and s2=5 and s4=9The Attempt at a Solution base case k = 3 s_3 <= 2s_1 + 3 5 <= 2+3 that is true. Now i must prove the inductive step. This is where I am having trouble. I assume that s_k <= 2s_{k-2}+3...

If we study model fit on a nonlinear regression model $Y_i=f(z_i,\theta)+\epsilon_i$, $i=1,...,n$, and in the Gauss-Newton method, the update on the parameter $\theta$ from step $t$ to $t+1$ is to minimize the sum of squares...

Is there a relationship between 1 and 2. If so, is it 1 implies 2, 2 implies 1, or if and only if. 1) $\operatorname{null}A=\operatorname{null}B$ 2) $\operatorname{col}\operatorname{rref}A=\operatorname{col}\operatorname{rref }B$

Homework Statement Given a Poincaré transformation, Lorentz+translation, I have to find the Poincaré generators in the scalar field representation and then prove that the commutation relations. I've done the first part but I can't prove the commutation relations. Homework Equations...

I have a designed feedback control system trying to minimize the overshoot and the setting time. The zeta I (think) ended up with is 0.94. According to this formula: I am supposed to have a very small overshoot. However the step response of the system looks like this: The poles are: 0.0000 +...

If three variables x,y and z are related via some condition that can be expressed as $$F(x,y,z)=constant$$ then the partial derivatives of the functions are reciprocal, e.g. $$\frac{\partial x}{\partial y}=\frac{1}{\frac{\partial y}{\partial x}}$$ Is the correct way to prove this the following...

While reading some articles on Wikipedia I came upon one interesting statement that essential says (I've rephrased for clarity; correct me if I'm wrong): "The Time-asymmetry of the second law of thermodynamics is due to the initial conditions of our universe" Can someone elaborate on what...