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    Estimating Rotational Temperature

    Homework Statement An R-branch of a band of a ^1\Sigma - ^1\Sigma of CO has its maximum intensity at J'=11. The internuclear distance is 1.1 Ǻ. Estimate the rotational temperature. Homework Equations My notes don't even really define what rotational temperature is. They say that the...
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    Use the Fourier transform directly to solve the heat equation

    Homework Statement Use the Fourier transform directly to solve the heat equation with a convection term u_t =ku_{xx} +\mu u_x,\quad −infty<x<\infty,\: u(x,0)=\phi(x), assuming that u is bounded and k > 0. Homework Equations fourier transform inverse fourier transform convolution thm The...
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    Solve the Dirichlet problem for the heat equation

    Homework Statement Solve the Dirichlet problem for the heat equation u_y=u_{xx}\quad 0<x<2\pi, \: t>0u(x,0)=\cos xu(0,t)=u(2\pi,t)=e^{-t} Homework Equations The Attempt at a Solution I have no idea what to do here. It seems to me like it's a mix of the solutions we learned. I...
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    Can someone explain this equality to me (complex variables)

    Homework Statement I hate to upload the whole problem, but I am trying to evaluate an indefinite integral, and I can follow the solution until right near the end. The example says that for a point on C_R|e^{-3z}|=e^{-3y}\leq 1. I don't understand how they can say this. Below is the question...
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    Need help finding a Laurent Series

    Homework Statement Let f(z) = \frac{1}{z^2-1}. Find Laurent Series valid for the following regions. • 0<|z−1|<2 • 2<|z−1|<∞ • 0<|z|<1 Homework Equations \frac{1}{1-z}=\sum^{\infty}_{n=0}z^n,\: |z|<1 f(z)=\sum^{\infty}_{n=0}a_n(z-z_0)^n+\sum^{\infty}_{n=1}b_n(z-z_0)^{-n} The Attempt at a...
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    Leibniz rule for differentiating an integral w.r.t a parameter

    Homework Statement I have the functionu(x,t)=\frac{1}{2c}\int^{x+ct}_{x-ct}g(\xi)d\xiwhere g is continuously differentiable and c is a constant. I need to verify that this is a solution to the wave equation. Homework Equations My prof gave me the...
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    Having trouble with CSC assignment. Trying to make an array of Strings

    Homework Statement I need to write a program that takes a text file, and looks for how many unique words it has, as well as the number of times they occur in the file. Homework Equations None The Attempt at a Solution public static void main(String[] args) throws FileNotFoundException...
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    Having trouble with this definition of a connected set

    Homework Statement My textbook gives me this definition of a connected set. http://media.newschoolers.com/uploads/images/17/00/69/80/76/698076.png [Broken] I have been working through my practice problems and I got to one that asked me to sketch the set given by|z+2-i|=2and note whether it is...
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    Is there any symmetry I can use to find this Fourier sine series?

    Homework Statement I am going over a practice exam, and I need to find the FSS of f(x)=x(\pi^2-x^2) Homework Equations f(x) \sim \sum^\infty_{n=1}a_n sin\left(\frac{n \pi x}{L}\right) a_n=\frac{2}{L}\int^L_0 f(x)sin\left(\frac{n\pi x}{L}\right)dx The Attempt at a Solution I think I...
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    Insulated boundary for circular laplace equation?

    Homework Statement Consider the Laplace’s equation, ∆u(r,θ) = 0, inside the quarter-circle of radius 2 (0 ≤ θ < π, 0 ≤ r ≤ 2), where the boundary θ is insulated, and u(r,\theta/2)=0 Show that the insulated boundary condition can mathematically be expressed as \frac{\partial u}{\partial...
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    Using a Fourier Cosine Series to evaluate a sum

    Homework Statement a) Show that the Fourier Cosine Series of f(x)=x,\quad 0\leq x<L is x ~ \frac{L}{2}-\frac{4 L}{\pi ^2}\left[\left(\frac{\pi x}{L}\right)+ \frac{\cos\left(\frac{3\pi x}{L}\right)}{3^2}+\frac{\cos\left(\frac{5 \pi x}{L}\right)}{5^2}+\dots\right] b) use the above series to...
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    Find arcsine(-2) using the rectangular representation of sin w

    Homework Statement Find \sin^{-1}(-2) by writing [tex]sin w = -2[/itex] and using the rectangular representation of \sin w Homework Equations Rectangular representation of \sin w The Attempt at a Solution I think my biggest problem here is I have literally no idea what the...
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    Can someone please explain to me what a dynamical trajectory means?

    Can someone please explain to me what a "dynamical trajectory" means? I am reviewing the first chapter of my classical mechanics book (Fetter & Walecka), and in the very first section he uses the term "dynamical trajectory". I have seen this derivation many times, but I just don't understand...
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    Derive the terrestrial equation of motion in the body-fixed frame

    Homework Statement Assume that the center of mass of the earth moves with approximately constant velocity with respect to the fixed stars, and that \mathbf{\omega}, the angular velocity of the earth, is constant. Rederive the terrestrial equations of motion...
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    (Complex analysis). Show that the inequality holds

    Homework Statement Show that the inequality\left|\frac{z^2-2z+4}{3x+10}\right|\leq3holds for all z\in\mathbb{C} such that |z|=2 Homework Equations Triangle inequality The Attempt at a Solution I'm not really sure how to go about this. the x is throwing me off. Should I write it out with...
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    Induced potential difference for disk spinning in magnetic field

    Homework Statement A solid conducting disk of radius a rotates about its symmetry axis with angular speed ω rads/s. If there is a uniform magnetic field \mathbf{B} perpendicular to the disk derive an expression for the potential difference induced between the centre of the disk and its rim...
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    Magnetic Field of A Toroid

    Homework Statement I'm working through a proof that says the magnetic field of a toroid is circumferential at all points inside and outside the toroid. I can follow most of the proof, but am a bit confused where the first equation comes from. Here is the figure from the textbook (Griffith's...
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    How to show a wave function satisfies the shrodinger eqn

    Homework Statement If a state is a linear combination of two energy eigenstates, does its wavefunction satisfy the time independent shrodinger equation? I guess in general, how would I show if the wavefunctions of a state does or does not satisfy the time-independent schrodinger equation...
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    Spin 1 Particle in a time dependant magnetic field

    Homework Statement https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-prn2/1483071_10151813160569290_1331827985_n.jpg Homework Equations \left|\psi ,t\right\rangle=\sum_i c_i(t)e^{-\frac{i E_n t}{\hbar}}\left|n\right\rangle The Attempt at a Solution I'm quite lost on how to even start this...
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    I really need a resource to explain the linear potential well to me

    So I am trying to learn this. It is not making sense to me. Every single resource I have found tells me I need to make some weird substitution, and then it becomes a differential equation that has the Airy equation as a solution, and then skips to finding the energy eigenvalues as a function of...
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    Separating a hamiltonian into C.O.M and relative hamiltonians

    Homework Statement Show that the two-body hamiltonianH_{\text{sys}}=\frac{\mathbf{p}_1^2}{2m_1}+\frac{\mathbf{p}_2^2}{2m_2}+V( \mathbf{r}_1,\mathbf{r}_2)can be separated into centre of mass and relative...
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    Potential and field of a thing circular ring

    Homework Statement I'm trying to work through an example in my classical mechanics textbook (Fowles and Cassiday, 7th ed, example 6.7.2. The problem I am having is when he expands the integrand into a power series. I'll write out the first part of the solution. The question is "find the...
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    Determining the damping constant from the ratio of amplitudes

    Homework Statement I have measured the amplitude between the first and tenth oscillations for a damped harmonic oscillator (spring with a mass attached). I also have measured the period. First question. Is an (underdamped) harmonic oscillator periodic? Like I know that the solution to the...
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    Matrix Representation of Operators

    Homework Statement This is quite a long problem, and I have most of it figured out, but I am getting stuck on the very last part of the problem. My problem is I do not understand how to find \left\langle\psi|a_1\right\rangle in the very last line. Is...
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    Basic Probability question for a spin 1/2 Particle

    Homework Statement A beam of spin-1/2 particles is prepared in the state \left|\psi\right\rangle=\frac{2}{\sqrt{13}}\left|+\right\rangle_x+i \frac{2}{\sqrt{13}}\left|-\right\rangle_x a) What are the possible results of a measurement of the spin component Sz, and with what probabilities...
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    Elementary Wave Functions

    Homework Statement A particle moving in one dimensions is in the state |\psi\rangle with position-space wave function \psi(x) = Ae^{−\lambda|x|} where A, λ are positive real constants. a)Normalize the wavefunction. b)Determine the expectation values of x and x^2 Homework Equations...
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    Double slit experiment intensity distribution

    Homework Statement I need to derive the intensity distribution of the double slit experiment. Intensity as a function of the slit separation d, the distance to the screen L and the wavelength \lambda. L>>d Homework Equations The Attempt at a Solution Ok this is ridiculous but...
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    Question about the jones matrix for a quarter wave plate

    Homework Statement So I need to identify the optical filter with jones matrix A=\frac{1}{sqrt{2}}e^{-i\pi /4}\left[\begin{matrix}1&-i \\ -i&1 \end{matrix}\right] Homework Equations See attempt The Attempt at a Solution So I have applied the rotation matrix like this ...
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    How do I show that a function defined by an integral is of class C1?

    Homework Statement F(x)=\int^{2x}_1\frac{e^{xy}\cos y}{y}dy Show that F is of class C^1, and compute the derivative F′(x). Homework Equations Thm: Suppose S and T are compact subsets of \mathbb{R}^n \text{ and } \mathbb{R}^m, respectively, and S is measurable. if f(\bf{x,y}) is...
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    Struggling with a chain rule problem

    Homework Statement Let (u,v)=\mathbf{f}(x,y,x)=(2x+y^3,xe^{5y-7z}) Compute D\mathbf{f}(x,y,z),\;\partial (u,v)/\partial(x,y),\;\partial (u,v)/\partial(y,z)\text{ and }\partial (u,v)/\partial(x,z) Homework Equations -chain rule The Attempt at a Solution well I can get...
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