# Search results

1. ### Constructing atlas

What do you mean (x^2+y^2+z^2 + R^2 - r^2)^2 = 4R^2(x^2+y^2). Sorry, I'm quite a novice
2. ### Constructing atlas

Well, the reason I bring up the two torus is because one of the sample problems in the book I'm using is to "prove that the two torus is a manifold by explicitly constructing an appropriate atlas." Well, I did fail to mention it need not be a maximal one.
3. ### Constructing atlas

Not a lot...It might help me to see simple examples like the two torus or a sphere...
4. ### 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.
5. ### 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...
6. ### 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...
7. ### 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...
8. ### 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...
9. ### 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...
10. ### 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...
11. ### 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...
12. ### 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...
13. ### 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...
14. ### 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?
15. ### Fourier Transfrom and expectation value of momemtum operator

Ok Thanks guys! That makes more sense
16. ### Fourier Transfrom and expectation value of momemtum operator

Um, ok. You're probably right. But I'm not sure I see what to do ...
17. ### 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...
18. ### Show that matrix A is not invertible by finding non trivial solutions

Ok. I think I got it. Thank you all for your quick replies!
19. ### Show that matrix A is not invertible by finding non trivial solutions

Sorry, I should have been more clear. That is what I meant.
20. ### Show that matrix A is not invertible by finding non trivial solutions

oh I see, if you try to eliminate one you end up eliminating all the others in the row as well
21. ### Show that matrix A is not invertible by finding non trivial solutions

hmm, you've given me something to think about. So I can see how B is not invertible because well Gaussian elimination on it fails, but what about C? I don't think you can immediately see it by trying to do the more familiar elimination steps, so is it enough to say that in a way it a dependent...
22. ### 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...
23. ### 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) /...
24. ### 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...
25. ### Contracting over indices chain rule

yeah you really don't have to use chain rule
26. ### Contracting over indices chain rule

Well if I do this (∂/∂t + ∂/∂x...)* each component of uβ there's still the uα I have to worry about. aα = duα/dτ so this seems to imply that uβ∂β = d/dτ which doesn't seem right...? And I'm not seeing how I can get that? Oh wait never mind...I think I got it! If say I transform into a rest...
27. ### 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...
28. ### 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...