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  1. B

    General Optics Question

    Homework Statement I have a compound thick lens problem that I need to find the sign of the refractive power. Homework Equations Thick lens equation and focal length equation. The Attempt at a Solution I believe all I need to do is calculate the focal length of the first two thick lenses and...
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    Relative Entropy or Kullback Leibler divergence

    Homework Statement I am suppose to calculate the relative entropy between two sets of data: Base set Set 1: A C G T 0 0 0 10 0 0 0 10 0 0 10 0 0 10 0 0 10 0 0 0 * * * * //Randomized 0 0 0 10 0 10 0...
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    Hidden Markov Model

    Homework Statement Consider an HMM with two possible states, “R” and “G” (for “regulatory” and “gene” sequences respectively). Each state emits one character, chosen from the alphabet {A,C,G,T}. The transition probabilities of this HMM are: aRG = aGR = 1/4 aRR = aGG = 3/4 The emission...
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    DNA sequence evolution

    Homework Statement A strand of length L begins life as all A's. Assume that each letter evolves independent of all the rest until today, 1000 generations later. Within each generation there is a ##\mu## probability that the letter mutates to either C, G, T. Finally, assume that once a letter...
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    DNA sequence modeled as 4 faced die

    Homework Statement I have a DNA sequence generated by L throws of a 4 faced die with probabilities ##\pi_A, \pi_C, \pi_G, \pi_T##. Each probability is unknown. Task: estimate the probability of each side of the die. Hint: use a random variable defined by the sequence that has a binomial...
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    Sequence Analysis (probability)

    Homework Statement I have a 4-letter DNA sequence (AGGA) that appears 10 times in a strand that is 1027 letters long. The probability of finding this sequence at any random position is 1/256. What is the Z-score of this observation? Homework Equations ##Z=\frac{(X-E(X))}{\sqrt{Var(X)}}## The...
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    Coin flip deal (stats/probability)

    Homework Statement Coin flip problem. I'm given the probability distribution of how many times a coin is heads out of 5 flips. From this, I need to determine if the following deal is worth it and, if not, how much it costs using variance: After flipping the coin 20 times I need to pay my...
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    Bloch sphere and mixed stats

    Homework Statement What is reduced density matrix ##\rho_A## and the Bloch vector representation for a state that is 50% ##|0 \rangle## and 50% ##\frac{1}{\sqrt{2}}(|0 \rangle + |1 \rangle)## Homework Equations The Attempt at a Solution [/B] I haven't seen many (any?) examples of this so...
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    Finite Temperature matrix

    Homework Statement Consider the Hamiltonian ##H=\begin{bmatrix} 0& \frac{-iw}{2}\\ \frac{iw}{2} & 0 \end{bmatrix}## Write the finite temperature density of the matrix ##\rho(T)## Homework Equations ##\beta=\frac{1}{kT}## The Attempt at a Solution The initial part of the problem had me find...
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    Double Well Potential

    Homework Statement Consider the Hamiltonian ##H=-\frac{d^2}{dx^2}+V(x)## ##V(x) =\begin{cases} \infty & x < 0 ,x>\pi \\V_0 & \frac{\pi}{2}-\frac{a}{2} \geq x \leq \frac{\pi}{2}+\frac{a}{2} \\ 0 &elsewhere\end{cases}## Use the boundary conditions at x=0 and x=##\pi## to set two of the...
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    Electron position at time t

    Homework Statement Consider the electron on a six site chain. The Hamiltonian is: ## H = \begin{pmatrix} 0 & -1 & 0 & 0 & 0& 0\\ -1 & 0 & -1 & 0 & 0& 0\\ 0 & -1 & 0 & -1 & 0& 0\\ 0 & 0 & -1 & 0 & -1& 0\\ 0 & 0 & 0 & -1 & 0& -1\\ 0 & 0 & 0 & 0 & -1& 0\\...
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    Compute e^(itH)

    Homework Statement Compute, using wolfram is an option, eitH where H is: ##H = \begin{pmatrix} 0 & -1 & 0 & 0 & 0& 0\\ -1 & 0 & -1 & 0 & 0& 0\\ 0 & -1 & 0 & -1 & 0& 0\\ 0 & 0 & -1 & 0 & -1& 0\\ 0 & 0 & 0 & -1 & 0& -1\\ 0 & 0 & 0 & 0 & -1& 0\\ \end{pmatrix}## Homework...
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    Time evolution, Hamiltonian

    Homework Statement A magnetic field pointing in ##\hat{x}##. The Hamiltonian for this is: ##H= \frac{eB}{mc}\begin{pmatrix} 0 & \frac{1}{2}\\ \frac{1}{2} & 0 \end{pmatrix}## where the columns and rows represent ##{|u_z\rangle, |d_z\rangle}##. (a) Write this out in Dirac...
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    Gaussian Wave packet

    Homework Statement Wave function of an electron: ##\frac{1}{N}∫_a^b[e^{ik_0x}(1+\frac{1}{2}e^{i\frac{0.1}{2}x}+\frac{1}{2}e^{-i\frac{0.1}{2}x})]dx## The integrand becomes zero both to the left and right of x = 0 . Let a be the first time it hits zero to the left and b the first time it...
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    Normalization of states

    Homework Statement These are rather simple questions but the rules for all of this are not quite clear to me yet. I'm to determine whether or not the following states are "legal" and if not I should normalize them. a. ##\frac{1}{√385} ∑_{x=1}^{10}x^2 |x>## b. ##\frac{1}{√2}...
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    Engineering Engineering Physics: 1 year left

    tl;dr: Computational Phys major with ~10 yr. industrial automation experience looking for guidance/suggestions for job search. Would prefer physics/astronomy oriented but know B.S. is limited in these fields. I'm about to start my last year of college at the UIUC Eng. Physics program (#1 in...
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    Field on a plane from line charge

    Homework Statement A wire at extends for -L to L on the z-axis with charge ##\lambda##. Find the field at points on the xy-plane Homework Equations ##E(r)=k\int\frac{\rho}{r^2}dq## ##k=\frac{1}{4\pi ε_o}## The Attempt at a Solution First time I've looked for field on a plane so I...
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    Comoving redshift and area of sphere

    Homework Statement Standard candles may be used to measure the "luminosity distance", using DL = (L/4F)1/2, where L is the source's intrinsic luminosity, and F is the observed flux. Inthis problem you will relate the luminosity distance to the previously discussed angular diameter...
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    Causal contact from opposite sides of Universe?

    Homework Statement No math required, mostly just a conceptual question. Consider two points at direct opposite sides of the expanding visible universe. Could these two points ever been in causal contact? Homework Equations The Attempt at a Solution I take causal contact to mean...
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    Eigenvector of complex Eigenvalues

    Homework Statement ##A=\begin{bmatrix} 16 &{-6}\\39 &{-14} \end{bmatrix}## Homework Equations The Attempt at a Solution I did ##A=\begin{bmatrix} 16-\lambda &{-6}\\39 &{-14-\lambda} \end{bmatrix}## and got that ##\lambda_1=1+3i## and ##\lambda_2=1-3i## The solution...
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    Flux through a Sphere

    I was told it might be better to post this here. Homework Statement The trick to this problem is the E field is in cylindrical coordinates. ##E(\vec{r})=Cs^2\hat{s}## Homework Equations ##\int E \cdot dA## The Attempt at a Solution I tried converting the E field into spherical...
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    Flux through sphere

    Homework Statement The trick to this problem is the E field is in cylindrical coordinates. ##E(\vec{r})=Cs^2\hat{s}## Homework Equations ##\int E \cdot dA## The Attempt at a Solution I tried converting the E field into spherical coords and I can find the flux that way but it is a...
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    Standard Candles

    Homework Statement Suppose that we observe the redshifts and apparent fluxes of a sample of standard candles. When observed at a distance of 1 Mpc, the standard candles are known to have a flux F1Mpc = 1. From this sample of standard candles, we can measure the Hubble constant H0...
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    Galaxy Mass with Dark Matter

    Homework Statement Suppose that a sprial galaxy has the mass profile: ##M_{disk}(r)=M_d[1-(1+\frac{r}{r_{rd}})e^{-\frac{r}{r_{rd}}}]## Where rrd=3Kpc. and Md is unknown. Like all galaxies, this galaxy also contains dark matter as well as its luminous matter. Using the rotational...
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    Multipying Determinants

    Homework Statement This is a practice problem where the solutions are given. Both are 3x3 matrices. det A=-2 and det B=1 find the following: 1)det(A6) 2) det(B-1A3B3AT) 3) det(4(AT)2(B-1)4) 4) det((2BT)-1) Homework Equations The Attempt at a Solution I get the first two...
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    B Field Inside of Sphere using Sep. Variables

    Done editing I hope. Homework Statement If Jf = 0 everywhere, then (as we showed in class), one can express H as the gradient of a scalar potential, W. W satisfies Poisson’s equation with ∇⋅M as the source. Use this fact to find the field inside a uniformly magnetized sphere. (Griffiths has...
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    Evaluating Scalar Field

    Homework Statement Evaluate the scalar field ##f(r, \theta, \phi)= \mid 2\hat{r}+3\hat{\phi} \mid## in spherical coords. Homework Equations Law of Cosines? ##\mid \vec{A} + \vec{B} \mid = \sqrt{A^2+B^2+2ABCos(\theta)}## The Attempt at a Solution I'm not sure the law of cosines...
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    Black Hole Accretion part 2

    Homework Statement This is the original problem for part 1 A) Suppose that a black hole of mass M accretes mass at a rate ##\dot{M}##. Further suppose that accretion of mass Δm leads to the radiation of energy ##\Delta E= \eta Δmc^2##, for some effeciency of energy conversion, ##\eta##. What...
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    Black hole Accretion Luminosity

    Homework Statement Suppose that a black hole of mass M accretes mass at a rate ##\dot{M}##. Further suppose that accretion of mass Δm leads to the radiation of energy ##\Delta E= \eta Δmc^2##, for some effeciency of energy conversion, ##\eta##. What is the luminosity of emitted radiation in...
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    Gravity of Event horizon

    Homework Statement I got a problem wrong on a quiz and I'm pretty positive on all the other questions as being correct but maybe this one.. How does the gravitational force at the event horizon (Schwarzschild radius) behave as the black hole mass increases? Homework Equations...
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