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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

    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

    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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    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

    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

    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

    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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    What is a pure quantum state and a mixed quantum state?

    hi what is a pure quantum state and a mixed quantum state? I looked up the internet but I did not quite understand. For pure quantum state I have read that they can't be written down as a mixture of other states??? are entangled states pure states?
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    Polar coordinates

    Homework Statement In the attachment, I do not understand how we got the second equation in terms of polar coordinates. Homework Equations The Attempt at a Solution I tried doing it by writing z_dot = (......)z and then plugging in r* exp i theta, but to no avail.
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    Bifurcation:topologically same?

    Hi I have not taken nay course in Topology. So can someone please explain what it means to say "in the neighborhood of some point bifurcation is topologically same"? thank you.
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    Quantum Mechanics: Matrices

    Homework Statement The problem is I am unable to understand the proof. I understand how it is done but I do not know how it is related to the theorem. It is probably because I am unable to understand the notation of matrices, the one involving k. It is given that I=δ_ij = 1 0 0...0...
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    Axis of rotation

    Homework Statement consider the following rotation matrix: 0 0 1 1 0 0 0 1 0 Find the axis of rotation. Homework Equations The Attempt at a Solution I know the following: Ω|1> = |2> Ω|2> = |3> Ω|3> = |1> where Ω is an operator. It is a cyclic permutation. What do not understand is...
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    Partial derivative and chain rule

    How is the double derivative equal to that in the equation 2 in the attachment? =|
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    Schrodinger cat

    Can we categorize the Schrodinger's cat as the chaotic system?:cool:
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    Curvature of a trajectory

    Hi! Can someone please explain how does the limit in the attachment equals the curvature of a trajectory? I do not understand it. Why is it defined this way? ζ=dx/dl and it is in the direction of T. Thank you!
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    Critical Points

    for cos y the critical points are n*pi - 0.5*pi for cos 2x, the critical points should be n/2 * pi - 0.25*pi because if I set y=2x = n*pi - 0.5*pi , I get the eq in red for x. However if I do it graphically, I just get n*pi - 0.25*pi. The question: why algebraically I am constrained to use...
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    Finding the roots!

    How would you find the roots of: b - tan (b) = 0 please do not that i have to plot the graphs of y=b and y=tan b and then i should find the solution. I want to know how to do it the other way. thank you
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    [coupled harmonic oscillators] old thread- need elaboration

    Hi Can someone please explain the answer to the following thread? I tried uncoupling the Hamiltonian but to no avail. https://www.physicsforums.com/showthread.php?t=602106 Thank you.
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    Differential and square of differential

    Hi I often see the following in books but I do not understand how they are equal. So can someone please tell me for what conditions does the following equality hold? (\frac{dy}{dx}) 2 = (d2 y)/(dx2)
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    Partial differential = the change?

    partial differential = the change?? Homework Statement How is Δy/Δx = \partial y / \partial x ? I just don't know the logic behind this.
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    Em waves in complex

    Homework Statement Moving in negative x-axis: E1 = E sin(wt + kx) Moving in right axis: E2 = Esin(wt-kx-θ) moving to right write complex representation The Attempt at a Solution E1= E Im(exp[i*(wt+kx)]) E2= E Im(exp[i*(wt-kx-θ)]) are these correct or do I have to take into...
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    Infinite square well energy

    Hi I have attached my attempt of solving the infinite square well for Energy. The value I get is different from that of the book, also in the attachment, Kindly explain if my answer is correct given the fact that I proceeded step by step and used no tricks. Thank you.
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    Operators Commutation

    Can someone please explain to me how do we get the following: [P(x), L(y)]= i h(cut) P(z) P(x) is the momentum operator with respect to x and L(y) is the angular momentum operator with respect to y. I have also attached the solution. I am stuck at the underlined part. I do not know how...
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    Answer confirmation-not an assignment question.

    Hi! I have attached the picture. Can someone please tell me what equation of motion will be? My guess is that it will be \ddot{x} = -k/x -kx/2
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    Damped oscillator- graphical interpretation

    Hi! The damped oscillator equation is as follows: x(t)= A exp(γt/2) cos(ωt) where ω= √( (w0)^2 + (γ^2)/4 ) I have attached a graph of a damped oscillator. The question is if I use graph to measure angular frequency, will it be w0 or ω? It should be w0 because if I put γ=0, I should...
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    Operators interpretation (Dirac notation)

    Hi all! If you are given an operator such that A|1> = √(1/3) |1> +√(2/3) |2>, how do we interpret it? I do know that 1/3 and 2/3 are probabilities but is this operator application on state one suggesting that this state in state 1 and 2 with probabilities 1/3 and /3 respectively? Thank you!
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    Bra-ket Notation and Operator

    Hi If C is an operator such that C|1> = |1> and C|2>=|2>, then C^3 |1>= |1>|1>|1> =|1> ^ 3 ? If yes, then what does this C^3 represent? :confused:
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