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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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    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

    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

    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!

    Suppose, there's an inclined surface, and a sphere, with radius R, is rolling without slipping. The Lagrangian is L = I \frac{\dot \theta ^2}{2} + m \frac{\dot s ^2}{2} - V where \theta is the angle of rotation of sphere and s is the curve length from top, and V is a potential which depends on...
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    Relativistic invariance

    In Feynman lectures in physics v2 28-6, Feynman points out that we can add a constant times \phi to D'Alembertian without distrupting the relativistic invariance. How and why?? Can someone work out a mathematical proof? Thanks in advance.
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    Laplace equation for parallel plate condersers

    I've recently started studying Laplace's equation and it's solution under various simple circumstances in electrostatics. I tried to solve the equation for a parallel plate condenser system, but I couldn't meet the boundary conditions. I had two plates, one placed on xz plane at y=0 (with...
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    Electrostatic pressure

    I have a metal sphere with the net charge q. And i'm trying to calculate the force that southern hemisphere exerts to northern hemisphere... and I get 0. now, the electrostatic "pressure" is \mathbf f = \sigma \mathbf E = (q/4\pi R^2) (q/4\pi \epsilon_0 r^2) \mathbf {e_r} due to the symmetry...
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    Degenerate perturbation theory question

    This's a question from Griffiths, about degenerate pertrubation theory: For \alpha=0, \beta=1 for instance, eq. 6.23 doesn't tell anything at all! What does it mean "determined up to normalization"?. Equations 6.21 and 6.23 involve 3 unknowns (\alpha, \beta, E^1), and Griffiths solved them...
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    Expectation values

    How much sense does it make to compute expectation value of an observable in a limited interval? i.e. \int_a^b \psi^* \hat Q \psi dx. rather than \int_{-\infty}^{\infty} \psi \hat Q \psi dx Apparently, it shouldn't make any sense for it gives weird results when you compute e.v. of momentum for...
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    DS/dt = -H?

    I'm trying to understand how \frac{\partial S}{\partial t} = -\mathcal{H}. I put the simplest/one dimensional Lagrangian (mv^2/2-V) and tried to derive it, but I failed: \frac{\partial S}{\partial t} = \frac{\partial }{\partial t} \int_{t_i}^{t_f} Ldt noting that x and \dot{x} is a function of...
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    Basic questions about QM computations

    1. How can we calculate expectation values of an arbitrary Q, even if \psi is not an eigenfunction of Q? 2. (Fourier transform related) Suppose I have piecewise wavefunction. \psi_{I} at (-\infty,-L), \psi_{II} at (-L,+L) and \psi_{III} at (L,+\infty). I can compute entire \phi(k) by taking the...
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    SE Lagrangian

    Euler-Lagrange equations for the Lagrangian density \mathcal{L} = V\psi \psi^* + \frac{\hbar^2}{2m}\frac{\partial \psi}{\partial x}\frac{\partial \psi^*}{\partial x} + \frac{1}{2}\left(i\hbar \frac{\partial \psi^*}{\partial t} \psi- i\hbar \frac{\partial \psi}{\partial t} \psi^*\right) gives...
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    Negative kinetic energy in tunneling

    Say I have a particle with a kinetic energy of 5 (in some units). And I have a potential barrier of 10 between 0<x<1 (again, in ome unit system), and 0 elsewhere. According to quantum theory, the partcile may be found between 0 and 1. And in this region, if the energy is conserved (5 = T + 10)...
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    Solution of hydrogen atom : legendre polynomials

    I was messing around with the \theta equation of hydrogen atom. OK, the equation is a Legendre differential equation, which has solutions of Legendre polynomials. I haven't studied them before, so I decided to take closed look and began working on the most simple type of Legendre DE. And the...
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    Legendre polynomials

    ...and orthogonality relation. The book says \int_{-1}^{1} P_n(x) P_m(x) dx = \delta_{mn} \frac{2}{2n+1} So I sat and tried derieving it. First, I gather an inventory that might be useful: (1-x^2)P_n''(x) - 2xP_n'(x) + n(n+1) = 0 [(1-x^2)P_n'(x)]' = -n(n+1)P_n(x) P_n(-x) = (-1)^n P_n(x)...
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    Motor driving

    I have quite a monster motor for a mini-hover craft. It requires quite much power. As a motor driver, i'm using a". The problem is it's output limited 2A, according to datasheet, while the driving voltage can be up to...
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    Lorentz force - conservative?

    \mathbf \nabla \times (\mathbf E + \mathbf v \times \mathbf B) pluggin stuff from Maxwell equations = -\frac{\partial B}{\partial t} + \mathbf v (\mathbf \nabla \cdot B) - \mathbf B (\mathbf \nabla \cdot v) Since \frac{\partial}{\partial t}(\mathbf \nabla \cdot \mathbf r) = 0 it's =...
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    How do transistors work?

    Yup. I've been looking around about it for a while, I delved into electronics books, they mention things like hole/electron flow, energy bands, but I haven't understood how transistors actually work. I've heard that diodes, transistors and other semiconductor materials involve tunneling, so...
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    Partial derivate philosophy

    partial derivate "philosophy" I'm having problems with fundementals of partial derivatives. I've looked around for something like "partial derivative FAQ", but couldn't find. Can any of the following be true in general? \frac{\partial f}{\partial x} = \frac{\partial f}{\partial...
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    Concerning series

    I wonder if there's any other series that can be used to approximate a function, other that Taylor/McLaurin and Fourier. For instance, can we expand a function in terms of Gaussians (Aexp(-bx^2))? Maybe something else?
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    Moment of intertia tensor

    I have an ellipse rotating around a fixed axis that passes through it's center, with a constant angular speed \omega. I'm being asked what torque would generate this motion. It should be \vec{\Tau} = \frac{d(I \vec{\omega})}{dt} = \dot{I} \vec{\omega} since angular speed is constant. I'm not...
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    Meaning of Lagrangian

    I've been thinking on it for a while, and can't find a satisfying argument. What would L=T-V mean physically? And what would it's time integral mean? What (physically what) are we minimizing? Following Feynman, it should be explained at freshmen level if we have understood it.
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    Deriving Dirac matrices

    I'm trying to linearize Klein-Gordon equation, following Dirac's nobel lecture: (E^2 - (pc)^2 - (mc^2)^2) \psi = 0 (E + \alpha pc + \beta mc^2) (E + \alpha pc - \beta mc^2) \psi = 0 Expanding the equations yields: -\alpha and \beta commutes with E and p -\alpha^2 = \beta^2 = 1 -\alpha...
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    Statistical mechanics -

    I've seen an approximation in a statistical mechanics book, given without any proof: \frac{<N!>}{<(N-n)!>} = <N^n> (1 + \mathcal{O}( \frac{1}{<N!>} )) I've been trying to work out a proof, but I'm simply stuck :yuck: any ideas how it can be proved?
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    Directional derivative

    Suppose I have a path \vec{r}(x,y) and some vector \vec{a}(x,y). Question is: how do I find the tangential and perpendicular component of a along the path r at a given point? For tangential component, I'd just take the projection of a on r with dot product (I guess this's correct). But what...