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  1. R

    Connection and tensor-issue with the proof

    Γabc are the christoffel symbols/connection and T^(bc) = (e^b,e^c)
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    Connection and tensor-issue with the proof

    Homework Statement I am tying to prove the following: \Gamma^{a}_{bc} T^{bc} =0 Homework Equations The Attempt at a Solution I approached this problem as follows: dx_{b}/dx^{c} * e^{a} (e^{b} . e^{c}) but it did not yield anything. Then I expanded the christoeffel symbols into...
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    StatMech: Binomial approximation

    I looked at the stirling formula derivation but I don't know how it is helpful here. So I have solved it the other way. [N-(n-(n-0))] [N-(n-(n-1))] [N-(n-(n-2))] [N-(n-(n-3))]......[N-( n-(3) )][N-( n-(2) )][N-( n-(1) )] For N>>n, using this approximation once, I get n terms: [N-n] [N-n]...
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    StatMech: Binomial approximation

    Homework Statement The question requires me to approximate binomial distribution to get poisson distribution. Show that N!/(N-n)!=N^n. Homework Equations N!/n!(N-n)! p^n q^(N-n)=Binomial distribution The Attempt at a Solution I expanded N!/(N-n)! and got...
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    QFT newbie-creation of particle and anti-particle

    Hi, I read the following in an online source: In relativistic settings, momentum and energy are equal so the uncertainty principle, for a particle of mass m which is trapped in a box of size L, becomes delta E>= \hbarc/L. If uncertainty exceeds delta E=2mc^2, we get pairs of particles and...
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    Tensor product: commutator for spin

    Homework Statement [S2 total, Sz ∅1] Homework Equations S2 total = S2∅1+ 1∅S2+2(Sx∅Sx+Sy∅Sy+ Sz∅Sz) The Attempt at a Solution I calculated it in steps: (1∅Sx 2 +Sx 2∅1) * Sz ∅1 =[S2x, Sz] ∅1 + Sz∅Sx 2 =-h_cut i (SxSy+SySx)∅1 + Sz∅Sx 2 Is it correct way of doing it? I...
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    QM: spin

    Of course it is a quantum number but why is there a half?
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    QM: spin

    Homework Statement Find the eigenvalues and eigenstates of the spin operator S of an electron in the direction of a unit vector n; assume that n lies in the xz plane. Homework Equations S|m>= h m|m> The Attempt at a Solution This question is from Zettili QM and they have...
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    Classical mechanics-coordinates

    In the book R_1 = R M2/ (M1 + M2) but mine is R1= R M2 / (M2-M1)
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    Classical mechanics-coordinates

    R= R_1 + R_2 where R_i is the distance to M_i from CM.
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    Moment of inertia tensor about y-axis of a cylinder.

    Homework Statement What must the ratio of height to radius of a cylinder be so that every axis is a principal axis (with the CM as the origin)? Homework Equations Moment of inertia tensor. I need I_yy = \sum m *(x^2 + z^2) The Attempt at a Solution I calculated I_zz = MR^2 /12...
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    Classical mechanics-coordinates

    CM= (R1m1+R2M2)/M1+M2 because CM=0, I get M1 R1 = -R2 M2 which further gives me R1= RM2 / (M2-M1) =|
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    Classical mechanics-coordinates

    Homework Statement Attached is the picture of a dumbbell. I do not understand how the coordinate of M1 is M2 R/ (M1 + M2) It is not an assignment question but an example from a book. Homework Statement Homework Equations The Attempt at a Solution
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    QM- matrix exponentiation

    Yes I found the the eigen basis.
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    QM- matrix exponentiation

    I will get the eigenvalues 1, -1, 0
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    QM- matrix exponentiation

    k* 0 1 0 1 0 1 0 1 0 That's the matrix of Ly for l=1.
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    QM- matrix exponentiation

    QM--- matrix exponentiation Homework Statement \ How do you go about exponentiating a 3*3 matrix? for example if you have <θ,∅|exp(-i*∅*Ly/h)|l,m> Homework Equations I know how to exponentiate a two cross two diagonalized matrix. you just exponentiate the diagonal terms...
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    Solve for r - inequality

    Homework Statement |4 + 2r - r^2| <1 Homework Equations 4 + 2r - r^2 = (r - (1+ √5) ) (r - (1 - √5)) The Attempt at a Solution I tried to use the roots but no use. How should I proceed?
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    Quantum Mechanics: k basis

    Could you please solve the solve question and suggest the steps?
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    Quantum Mechanics: k basis

    Yes, I know that. I simplified things and I got that answer.
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    Quantum Mechanics: k basis

    I introduced the identity twice and on simplifying, I get 1/2pi ∫∫dk dx ??
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    Quantum Mechanics: k basis

    I am getting a very weird answer.
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    Quantum Mechanics: k basis

    <k|x>= exp(-ikx)/(2*pi)^0.5
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    Quantum Mechanics: k basis

    Homework Statement write the following in K basis: A=∫|x><x|dx where the integral limits are from -a to a Homework Equations The Attempt at a Solution I tried solving it by inserting the identity I=∫|k><k|dk where the integral limits are from -∞ to +∞ but then I do not...
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    Procedure to draw a phase portrait by hand ?

    @HallsofIvy: Thank you so much! That was such an elaborate reply! helped me a lot!
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    Bifurcation:topologically same?

    If you compare both sides of the bifurcation point, they are topologically same.
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