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    Fourier Properties (shifting)

    Hi, I need help with some basic fourier transform properties stuff - its fairly simple though I think I am doing something wrong. So we know from the shifting property if h(x) has the fourier transform H(f) then h(x-a) has the fourier transform H(f)ei*2*π*f*a so I have the function cos(2πf0x...
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    Wave function at infinity

    Homework Statement If I have a wave function that goes to infinity can I assume that the derivative also goes to 0 at infinity? Homework Equations The Attempt at a Solution The reason I think it does is because the wavefunction and its derivative must be continuous everywhere...
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    Average energy mass on a spring

    Homework Statement Hi, I hope this isn't a silly question. I am looking to find the mean potential energy of a mass on a spring with spring constant k and maximum displacement x0. Homework Equations The Attempt at a Solution I know the maximum energy is 1/2*kx0^2 so would the...
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    Quantum well combination

    Homework Statement The question is attached as a picture. Note: if someone would prefer I type it out I can. Homework Equations Schrodingers equation The Attempt at a Solution PART A I am pretty sure I got the well right. It looks like a finite well inside an infinite well. I...
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    Stirlings approx/CoinFlips/Gamma function

    Homework Statement Hi I actually have three questions that I am posting here, help in all of them would be greatly appreciated! 1) Prove that ln(n!) ≈ nln(n)-n+ln(2*pi*n)/2 for large n 2)Supposed you flip 1000 coins, what is the probability of getting exactly 500 heads 3) Show that n! =...
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    Estimate energy of infinite well (ground state)

    Homework Statement We have to estimate the ground state energy of an infinite potential well (1d) using an argument based on the heisenberg uncertainty principal. We then are supposed to compare it with the exact value from the eigenvalue equation. Homework Equations Below The...
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    Planck Black-Body Law

    Homework Statement Starting from the Planck-Body Law I_{λ}dλ = \frac{2\pi c^{2}h}{λ^{5}} \frac{1}{e^{hc/(λkT)} - 1}dλ where λ is the wavelength, c is the speed of light in a vaccuum, T is the temperature, k is Boltzmann’s constant, and h is Planck’s constant, prove that the total energy...
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    Free Current

    Homework Statement I am looking at an example problem in the text and they skipped some steps. I think I am missing somthing obvious but none-the-less I don't know what is going on. We have a long copper rod o radius R which carries a uniformly distributed (free) current I. Find H, the...
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    Determining Wave Equation

    Homework Statement One end of a long horizontal string is attached to a wall, and the other end is passed over a pulley and attached to a mass M. The total mass of the string is M/100. A Gaussian wave pulse takes 0.12 s to travel from one end of the string to the other. Write down the...
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    Energy of a system

    Homework Statement There are 2 long coaxial insulating cylinder. The inner and outer cylinders have radii of a and b and charge densities λ and -λ uniformly distributed on the surface. Calulcate energy per unit length 2 ways (equations below) Homework Equations W = \frac{1}{2}\int σ...
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    Simple Harmonic Motion

    Homework Statement Two-dimensional SHM: A particle undergoes simple harmonic motion in both the x and y directions simultaneously. Its x and y coordinates are given by x = asin(ωt) y = bcos(ωt) Show that the quantity x\dot{y}-y\dot{x} is also constant along the ellipse, where here the...
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    Divergence physics homework

    Homework Statement In deriving the formula div v = \frac{∂v_{x}}{∂x} + \frac{∂v_{y}}{∂y} + \frac{∂v_{z}}{∂z} we used a rectangular solid infinitesimal volume; however, any shape will do (although the calculation gets harder). To see an example, derive the same formula using the prism-shaped...
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    Magnetic field from vector potential function using tensor notation

    Homework Statement We will see (in Chap. 5) that the magnetic field can be derived from a vector potential function as follows: B = ∇×A Show that, in the special case of a uniform magnetic field B_{0} , one possible vector potential function is A = \frac{1}{2}B_{0}×r MUST USE TENSOR NOTATIONm...
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    Flux and Divergence

    Homework Statement This is a coursework problem. I am having issues understanding the concepts on this one topic - divergence and how it relates to flux. I have attached screenshots that honestly give the best representation of my issue but I will set up the issue I am having...
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    Using Matlab to do basic convultions

    Homework Statement This is more of a imaging/physiological course but it uses convolutions and i can understand the applications, i just need help writing the matlab script to give meaningful answers. The problem asks that we use matlab to convolute 2 functions: x(t) = a*tb*exp(-ct)...
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    Rotational momentum (conservation problems)

    1.A rigid structure consisting of a circular hoop (on the right) of Radius R and mass m, and a square (on the left) made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a verticle axis, with a period of rotation of 2.5 s. Assuming R = 0.50m...
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