Recent content by RawrSpoon

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    System of Two Quantum Particles

    Ahhhh it makes sense now. The reason the distinguishable particles is Z(\beta , 2) = (1+e^{-\beta \varepsilon})^{2} is because expanding the expression gives two different states where E_{i}=\varepsilon right? That means that for fermions, Z=e^{-\beta \varepsilon} since E_{i} can ONLY be...
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    System of Two Quantum Particles

    Ok so then Z(\beta , N) = \sum_i e^{-\beta E_{i}} = (e^{-\beta (0)})+(e^{-\beta \varepsilon})+(e^{-2 \beta \varepsilon}) I assume that E_{i} is the total energy of each microstate, so given the microstates {AA,0}{A,A}{0,AA} I assume the energy is 0, \varepsilon, and 2 \varepsilon Is this...
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    System of Two Quantum Particles

    Homework Statement Consider a system of two quantum particles. Each particle has two quantum states, one with zero energy and one with energy ε>0. For each of the three cases, draw a table of the possible microstates α of the system, and find the canonical partition function Z(β). a)The two...
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    Harmonic Oscillator and Volume of Unit Cell in Phase Space

    I seem to have just copied E incorrectly from my paper, but I have exactly what you mentioned on my paper, so sorry about the mixup! Gotcha, so multiplying by 1/2 is incorrect. This makes sense, since upon reflection on your response, I've concluded that multiplying by 1/2 was a mistake. Thank...
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    Harmonic Oscillator and Volume of Unit Cell in Phase Space

    First off, thank you so much for replying! I did some progress on this, I'm not sure if it's right. So I did something similar, albeit x=\frac{\beta \hbar \omega}{2} This gave me Z_{qm}(T) = \frac {e^{-x}}{1-e^{-2x}} = \frac {1}{e^{x}-e^{-x}} = \frac {1}{2 sinh(x)} = \frac {csch(x)}{2} I...
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    Harmonic Oscillator and Volume of Unit Cell in Phase Space

    Long time no see, PhysicsForums. Nevertheless, I have gotten myself into a statistical mechanics class where the prof is pretty brutal and while I can usually manage, this problem finally has me stumped. I'd like to be nudged in the right direction, not outright given the answer if possible. I...
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    Charged massive particle reacting to EM wave

    If I'm understanding you correctly, that means that C1 is 0, right? At least for these purposes. As such I get that F_{mag}=\frac{q^2E_0^2}{mc(\gamma^2+\omega^2)}\Big(\gamma cos^2(kz-\omega t)-\omega sin(kz-\omega t)cos(kz-\omega t)\Big)\hat{z} Which would give me an average of...
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    Charged massive particle reacting to EM wave

    Funnily enough I JUST tried it about 30ish minutes ago. I think I did it wrong though, it's kind of a large equation and, to be fair, I let Mathematica solve it for me. Anyway, I tried the following m\frac{dv}{dt}+\gamma mv=qE_0cos(kz-\omega t) which led me to v(t)=\frac{qE_0}{m(\gamma ^2+\omega...
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    Charged massive particle reacting to EM wave

    Homework Statement Consider a particle of charge q and mass m, free to move in the xy plane in response to an electromagnetic wave propagating in the z direction (might as well set δ to zero) a) Ignoring the magnetic force, find the velocity of the particle, as a function of time. (Assume the...
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    Calculating Force using the Maxwell Stress Tensor

    Homework Statement Calculate the force of magnetic attraction between the northern and southern hemispheres of a uniformly charged spinning spherical shell, with radius R, angular velocity ω, and surface charge density σ. Use the Maxwell Stress TensorHomework Equations F=\oint \limits_S \...
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    Total energy and power of electromagnetic fields

    Nevermind, I solved it after all! I used my original method by finding the sum of the two components of work and realized that the volume element in cylindrical coordinates is s ds d\phi dz so I solved the integrals that way, which gave me a variation of the solution. I had completely forgotten...
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    Total energy and power of electromagnetic fields

    Homework Statement Consider the charging capacitor in problem 7.34 (A fat wire, radius a, carries a constant current I, uniformly distributed over its cross section. A narrow gap of wire, of width w, w<<a, forms a parallel-plate capacitor) a) Find the electric and magnetic fields in the gap, as...
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    Applying the Biot-Savart Law to solenoids

    I hadn't done one like that problem actually so thank you so much for that! And I'm a little disappointed the integrals are very difficult by hand, but at least now I know a little better when to use Ampere's Law. Thank you.
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    Applying the Biot-Savart Law to solenoids

    Not really homework but I figured this was the best place to post anyway. 1. Homework Statement I want to find the magnetic field B for an arbitrary solenoid using the Biot-Savart Law. I can find it easily through Ampere's Law, but I'd like mastery over the Biot-Savart Law. Homework Equations...
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    Projectile Motion from a height with Air Resistance

    Hey all, me again. This time my question has to do with projectile motion with air resistance from a given height. Homework Statement A cannon is located on a cliff of height h. If the muzzle velocity of a projectile is v0, find the range of the projectile when the drag is proportional to the...
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