Recent content by gulsen

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    Electrons distinguishable ?

    They are, as a matter of fact, indistinguishible. Of course their dynamical properties differ, but indistinguishible means you cannot a priori know which one has that particular property. That is to say, if you somehow know that one electron has spin up, and other has spoin down, the...
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    Grover's Algorithm: is it really a search algorithm

    I'm wondering how it really is useful. The input for the, say 2-qubit, quantum computer that is running Grover's algoritm is |\Psi \rangle = (|1 \rangle + |2 \rangle + |3 \rangle + |4 \rangle) / \sqrt{4} And let us say we're looking the 3rd element in the so-called database. Now, Grover...
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    Gas with interacting molecules (from goldstein)

    Homework Statement (from Goldstein, problem 3.12) Suppose that there are long-range interactions between atoms in a gas in the form of central forces derivable from potential U(r) = \frac{k}{r^m}, where r is the distance between any pair of atoms and m is a positive integer. Assume further...
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    Where do electrons go while making a quantum jump?

    Electron may be somewhere near the nucleus or in Hawaii. I'd also like to add that electron is, as far as we know, a structureless point particle. What is smeared out is the wave-function associated with it. When you go measure it, you'll find that it's a point particle. The abrupt "quantum...
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    Probabilistic interpretation of wave function

    The star means complex conjugate: replaces all is with -is. In your case, \psi^* = A^* sin(\pi x / L), but you can takeA to be real, making \psi = \psi^*.
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    A problem from Sakurai

    Homework Statement (Sakurai 1.27) [...] evaluate \langle \mathbf{p''} | F(r) | \mathbf{p'} \rangle Simplify your expression as far as you can. Note that r = \sqrt{x^2 + y^2 + z^2}, where x, y and z are operators. Homework Equations \langle \mathbf{x'} | \mathbf{p'} \rangle = \frac{1}{ {(2 \pi...
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    Equation for S from state func and C

    Solved it.That equation I wrote will have an integration factor f(V). Using \frac{\partial S}{\partial V}_T = \frac{\partial P}{\partial T}_V, we have the solution for S, this time with an integration factor of T. By compraison of these two statements of S, it's perfectly defined.
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    Equation for S from state func and C

    Heat capacity of a liquid is C=T^4 and the state function is V(T,P) = Aexp(aT-bP) Derive an equation for entropy. Use the relevant Maxwell relations. dU = T dS - PdV \frac{\partial U}{\partial T}_V = C = T^4 \Rightarrow U = \frac{T^5}{5} + f(V) Since it's a liquid, and there're no...
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    Transmission amplitude using path-integrals

    Hello, As a path-integral newbie, I've been trying to calculate the amplitude for an electron which enters a box (potential within the box is given) at a point to emerge the other edge of the box (it doesn't matter when it exits). For simplicity, I first tried to work out the problem in one...
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    Intiutive approach to Green's function for SE

    Griffiths develops an intelgral equation for Scrödinger equation in his QM book. As doing so, he requires Green's function for Helmholtz equation (k^2 + \nabla^2) G( \mathbf r) = \delta^3(\mathbf r) A rigourious series of steps, including Fourier transforms and residue integrals follow...
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    Free Particle Action

    I've recently started Feynman & Gibbs. I was sure exercises will be fun, but i can't enjoy myself when i fail solving the first one! Exercise 1-1 says: show that free particle action is \frac{m}{2} \frac{x_b^2 - x_a^2}{t_b-t_a} I tried finding anti-derivative of \dot x^2, ended up with...
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    Induced E by a solenoid with time-varying current

    Cylindrical solution gave a better insight though. Since the system is symmetric around z-axis, the electric field should be independent of \theta, therefore, the solution is \mathbf E = -k \left(\frac{s}{2} \mathbf e_\theta \right). Wish that I had a more rigorous way to show it, though.
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    Induced E by a solenoid with time-varying current

    Thanks for the replies! Meir Achuz, I'd ask "why?" In cylindirical coordinates, z-component of curl is \frac{1}{s} \left( \frac{\partial (s A_{\theta}) }{\partial s} -\frac{\partial A_s}{\partial \theta} \right) = -k which has again 3 mathematically possible solutions -k/2(\frac{s}{2}...
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    Induced E by a solenoid with time-varying current

    Imagine a solenoid with n turns per length. Now, for an instant, in which everything looks static, the magnetic field inside the solenoid will be n \mu_0 I \mathbf e_z (choosing solenoid alinged with z-axis), and zero field outside. Now, what would happen if we change the current in time? To...
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    Point particle Lagrangian paradox!

    Thanks for the replies! I think i've developed a clear answer to the "paradox": The point particle configuration assumes no friction, the object freely slides under the gravity. However, in the rolling ball configuration, the is a friction, and it's responsible for the torque which causes...