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    Constructing atlas

    I'm trying to get a better understanding of some topology for a GR class I'm taking...I'm wondering if someone can help me understand how to go about constructing atlases or just charts in general. I understand the concept but I am trying to get a better handle on the math.
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    Energy and the Friedmann Equation

    Homework Statement To relate E to the total energy of the expanding sphere, we need to integrate over the sphere to determine its total energy. These integrals are most easily carried out by dividing the sphere into shells of radius r, and thickness dr, so that each shell has a volume dV...
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    Quantum Rigid Rotor

    Homework Statement Consider a rigid rotor with moment of inertia Ix = Iy = I, Iz = (1 + ε)I Classically, his energy is given by, E = L^2/2I. (c) What are the new energy eigenstates and eigenvalues? (d) Sketch the spectrum of energy eigenvalues as a function of ε. For what sign of do the...
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    Eigenvalues of unitary operators

    Homework Statement We only briefly mentioned this in class and now its on our problem set... Show that all eigenvalues i of a Unitary operator are pure phases. Suppose M is a Hermitian operator. Show that e^iM is a Unitary operator. Homework Equations The Attempt at a Solution...
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    Double Delta function potential well

    Consider a one-dimensional system described by a particle of mass m in the presence of a pair of delta function wells of strength Wo > 0 located at x = L, i.e. V(x) = -Wo (x + L) - Wo(x - L) This is a rough but illuminating toy model of an electron in the presence of two positive. charges...
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    Confirmation concept questions eigenfunctions and operators

    Homework Statement Are the momentum eigenfunctions also eigenfunctions of e free particle energy. Operator? Are momentum eigenfunctions also eigenfunctions of the harmonic oscillator energy operator? An misplayed system evolves with time according to the shrodinger equation with potential...
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    How do I study for this exam?

    Homework Statement I've never had an exam before in this format. It's 50-min long for Quantum I. It will be mostly short answer with small computations. It's supposed to test our conceptual understanding. I've been reviewing my notes, making sure I harp on the central ideas of quantum...
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    Mass planetary formation calculation?

    Homework Statement Compute the mass of volatile material (specifically just H and He) not accreted by the Earth. Assume the mass accreted by the Earth is 7e23 kg. How does the mass of the missing volatiles compare with the actual mass of the Earth? Use the following table: Principal...
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    Formal properties of eigenfunctions

    Homework Statement Give a physicist's proof of the following statements regarding energy eigenfunctions: (a) We can always choose the energy eigenstates E(x) we work with to be purely real functions (unlike the physical wavefunction, which is necessarily complex). Note: This does not mean...
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    Finding basis of 3x3 matrix space

    Homework Statement For my homework assignment, I'm supposed to find a basis for the space of 3x3 matrices that have zero row sums and separately for zero row columns. I am having a hard time with this as it seems to me that there are a lot of combinations I have to consider. For the first...
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    Quick question about Dirac delta functions

    What does the square of a Dirac delta function look like? Is the approximate graph the same as that of the delta function?
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    Fourier Transfrom and expectation value of momemtum operator

    Homework Statement Using <\hat{p}n> = ∫dxψ*(x)(\hat{p})nψ(x) and \hat{p} = -ihbar∂x and the definition of the fourier transform show that <\hat{p}> = ∫dk|\tilde{ψ}(k)|2hbar*k 2. The attempt at a solution Let n = 1 and substitute the expression for the momentum operator. Transform the...
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    Show that matrix A is not invertible by finding non trivial solutions

    Homework Statement The 3x3 matrix A is given as the sum of two other 3x3 matrices B and C satisfying:1) all rows of B are the same vector u and 2) all columns of C are the same vector v. Show that A is not invertible. One possible approach is to explain why there is a nonzero vector x...
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    Integration help, Kepler's problem Lagrangian dynamics

    Homework Statement Carry out the integration ψ = ∫[M(dr/r2)] / √(2m(E-U(r)) - (M2/r2)) E = energy, U = potential, M = angular momentum using the substitution: u = 1/r for U = -α/r Homework Equations The Attempt at a Solution This is as far as I've gotten: -∫ (Mdu) /...
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    Help with a mechanical lagrangian problem

    Homework Statement We are given L = 1/2mv2 - mgz. a) Find the equations of motion. b) Take x(0) [vector] = 0; v(0) [vector] = v0 [vector] ; v0z > 0 and find x(τ) [vector] and v(τ) [vector], such that z(τ) = 0;  τ≠0. c) Find S. Homework Equations Euler-Lagrange equation and...
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    Contracting over indices chain rule

    Homework Statement As part of a problem I am doing I am asked to show uβ∂βuα = aα where u is 4 velocity and a refers to 4 acceleration. The way to do this is not immediately obvious to me, especially since the problem implies there should be a chain rule step involved which I am not seeing. I...
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    Perfect fluids and the stress energy tensor

    Homework Statement "Texbooks that describe perfect fluids are often a little unclear about what is being assumed. It may not be immediately obvious why can't the pressures be different in different directions? Let's examine this. Suppose Tαβ = diag(ρ,(1+ε)P,P,P) . Show that if one performs a...
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    Radiation pressure

    Homework Statement I have an exam on Monday and I'm trying to get a few concepts straight before then. I have a few questions... 1) p = E/c for a photon. Is this also true for a wave? 2) Assuming complete absorption, radiation pressure is 1/c x Poynting vector. What happens when there's...
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    Assistance on a recursive proof

    Homework Statement Define a sequence of numbers Ai by: A0 = 2, An+1 = An/2 + 1/An (for n greater than or equal to 1). Prove that An less than or equal to √(2) + 1/2n for all n greater than or equal to 0. I think it's a safe bet that induction should be used here. I'm having trouble finding the...
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    Euler Equation to Compute Extreme?

    A problem on my homework: We learn early on that "the shortest distance between two points is a straight line." Let's prove it...Using the Euler equation, compute the extrema of ∫sqrt(1 + (dy/dx)2)dx from x1 to x2 ...show that this corresponds to lines "y = mx +b". Euler had a lot of...
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    Resistor cube

    Homework Statement I am looking at the classic resistor cube problem-the one in which there is a cube with resistors all of the same value on each side. Particularily I am having trouble understanding the symmetry argument for the case in which the current enters and exits across the...
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    Relativistic electric field derivation

    Homework Statement I am supposed to derive this equation: tan(phi) = γtan(θ) by performing an integration to find the flux of E through each of 2 spherical caps; the flux through each of these caps should be equal. The first cap spans the angle θ; the element of surface area may be taken as...
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    Faraday's experiment

    Homework Statement The coils which first produced a slight but detectable kick in Faraday's galvanometer he describes as made of 203 feet of copper wire each, wound around a large block of wood. The turns of the second spiral (that is, single layer coil) were interposed between those of the...
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    Calculating the potential energy of a uniformly charged sphere

    Homework Statement The sphere has a radius a and is filled with a charge of uniform. They way I am asked to do this is by building the sphere up layer by layer. And I know that the field outside the sphere is the same as if it were a point charge. Homework Equations U = ε/2∫E^2 dv The...
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    Electric field of two point charges

    Homework Statement Two point charges Q and -Q are separated by a distance d. The point p forms an equilateral triangle with the two charges of side length d. Find the magnitude and direction of the electric field at point p. What is the electric potential at P? Then, a charge of 2Q is placed...
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    Having trouble coming up with this equation

    Homework Statement cupric bromide is heated. I know I should get cuprous bromide and bromide vapor is this right? CuBr2 --> CuBr + Br2 ? then, nitric acid is added to the cuprous bromide CuBr + HNO3 --> ? This is heated...I know I should get CuO... then the CuO + CH4 --> Cu + H2O...
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    Looking for Anti-derivative?

    Homework Statement a9t) = 1.2t. If v(1) = 5m/s, v(2) = ? If x(1) = 6m, x(2) = ? Homework Equations The Attempt at a Solution I know (anti-deriv) that is something like v(t) = .6t^2, but plug in 1 and that's not 5m/s?
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    Free Fall help

    Homework Statement An alert hiker sees a boulder fall from the top of a distant cliff and notes that it takes 1.3s for the boulder to fall the last 3rd of the way to the ground. Ignore air resistance.a) what is the height of the cliff in meters? b) If in part a) you get 2 solutions what does...
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    Vertical Drop rides at amusement parks

    Homework Statement Has anyone ever been on one of these. (I admit I have always been too chicken.) Can anyone explain to me what was felt at the bottom of the first drop and the physics why that was so. Also, estimate the time when the car began to slow down as a fraction of the total...
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    Circular Motion help please

    Homework Statement A 171 kg roller coaster car is on a track that forms a circular loop of radius 45.9 m in the vertical plane. If the car is to just maintain contact with track at the top of the loop, what is the minimum value for its net inward acceleration at this point? On the Round...
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