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If you know these are free particles (i.e. potential energy term in the Hamiltonian is 0) then the best start would be to calculate the N particle partition function, it's usually called Z or QN. Once you have the partition function, the Helmholtz free energy is given by: A(N,T,V) = -kTln(Z)...

Yeah, I just caught the potential energy problem myself and fixed it. However, I'm not quite sure what you mean about not needing to carry out the total time derivative. In the equation for Φ, ∂L/∂Φ = 0, so this would mean that the physical quantity described by (d/dt)(∂L/∂Ω) is conserved. Am I...

Homework Statement Find the Lagrangian and equations of motion for a spherical pendulum Homework Equations L=T-U and Lagrange's Equation The Attempt at a Solution [/B] I found the Lagrangian to be L = 0.5*m*l2(ω2+Ω2sin2(θ)) - mgl*cos(θ) where l is the length of the rod, ω is (theta dot)...

I'm also not an astrophysicist, but I have worked with some and I can say that having some background in computation is very helpful. i.e. computational physics, coding, model making, etc.

I can give some personal experience on the matter, but not your exact situation. For a bit of back story, I applied for the NSFGRFP after my senior year of undergrad as I was applying for graduate school. At the time, I had 2 and a half years of research experience, one first-authored paper, one...

Often, the hardest part about some of the introductory physics problems is figuring out what you're being asked and how to proceed with a solution, not necessarily the solution itself. Don't worry about failing, but I agree with MidgetDwarf: you definitely need a really solid grasp of all of the...

Hi all, I'm starting graduate school and really need a better handle on computational physics. I'm not extremely experienced with MATLAB and haven't used Python or anything else. Does anyone know a good textbook to get me started? I looked in the textbooks links to this forum thread and the...

î + ĵ + √2k̂ is a vector made up of three components, but it corresponds to a single vector. From my interpretation of the question, I would assume the question expects three answers (which is seems like it does). Rather than finding the angle î + ĵ + √2k̂ makes with î + ĵ + k̂ you are finding...

I believe what he means in regards to the consideration of the presence of an eather is that all waves travel in some medium. It was reasonable to say that if every other type of wave travels through a medium, light must as well. However, looking out in space, near vacuum, there is no such...

You can even do Young's double split experiment with single photons and still observe the diffraction pattern on the back screen. Thus, you can describe the photons as waves. Yet, if you tried to measure which slit the photon was going through, you lose this diffraction pattern on the back end...

I am a first year graduate student in physics and am becoming familiarized with Raman spectroscopy to study structure of materials based off of their vibrational states. In some personal study outside of this, I came across the idea of inelastic electron tunneling spectroscopy (IETS) and was...

Update: I should probably transform to coordinates like (r,theta) and find theta dot, right?

Homework Statement We have a particle of mass m moving in a plane described by the following Lagrangian: \frac{1}{2}m((\dot{x}^2)+(\dot{y}^2)+2(\alpha)(\dot{x})(\dot{y}))-\frac{1}{2}k(x^2+y^2+(\beta)xy) for k>0 is a spring constant and \alpha and \beta are time-independent. Find the normal...

In general, I believe pictures always make this more intuitive and easy to understand. If you drew a picture of the case you presented in the original post, it would be evident that the two points lie on the same horizontal line. In this case, your method works. However, in the case I gave as...

You can do this for this example. With how you described it, it like taking the x-axis. There, you would be setting the 0 point at the origin, such that any distance westward (in your case, the 23m) is negative and anything eastward positive, which is legitimate. The only time this may get a bit...

Thanks for the reply. So building off of this, if we want to use parallax to measure more and more distant objects (say stars), the best way to get resolution is to put telescopes in space with larger and larger orbits around the sun/earth? If so, it makes it rather evident why we don't use...

I would like to preface this by stating that I am not very well-versed in cosmology or astrophysics, but I've been thinking: I understand the idea of parallax, both in the sense of human eyes measuring distances to nearby objects and in the sense of telescopes on Earth (or in orbit) measuring...

As a rule of thumb, take your answer out to the number of significant digits given in the problem. For example, if you are given that some quantity of the problem equals 0.751, you were given three significant figures. Thus, if you put something in your calculator and get an answer out to 10...

Would that mean the charge distribution is zero? Yes. A good way to check this is to apply Gauss' law to the electric field you calculated. It is extremely simple to show that the divergence of E goes to zero in this case, so that automatically implies that net charge is zero. You stated in...

This isn't a precise homework question, but this seemed like the most reasonable place to post. If not, please feel free to move it. I have a large set of data points that should fit to a known equation (the Drude-Smith model for conductivity) The equation the data should fit to is: σ(ω) =...

Before I get into my question, it is helpful to note the paper I am referring to. "Photovoltage in nanocrystalline porous TiO2" by V. Duzhko, et al. DOI: 10.1103/PhysRevB.64.075204 In Section B. "Spectral photovoltage in well-passivated porous TiO2 layers", the authors mention that "The...

According to Einstein's relativity, any object with mass cannot move at the speed of light. Since a photon moves at the speed of light, its mass is zero, therefore the equation E2 = (pc)2+(mc2)2 reduces to E=pc where p is the momentum of the photon. In the textbook "Modern Physics" by...

Homework Statement I am working on a little project in which I analyze a video I found online and try to determine if it is real of a hoax. The video I am analyzing includes a man throwing a football off of a football stadium (at the very top) and making it into a basketball hoop at field...

Homework Statement A mass m = 750 g is connected to a spring with spring constant k = 1.5 N/m. At t = 0 the mass is set into simple harmonic motion (no damping) with the initial conditions represented by the point P in the phase space diagram at the right. **(This phase space diagram has...

There is nothing specifically we talked about in class (We haven't really done any proofs at all - we have just talked about Sentential Logic, truth tables, and basic set theory stuff). Although we haven't really covered proofs in class yet, it is considered a "proofs class" so he wanted us to...

Homework Statement Show that if m and n are integers such that 4|m2+n2, then 4|mn Homework Equations The Attempt at a Solution Since 4 divides m2+n2, then we can say that m2+n2 = 4k, where k is an integer. I haven't done any mathematical proofs of any kind yet, but we were supposed to see...

So if you know that b = -2c, and you know that a+b+c = 0, then a = c. This means that the vector A is made up of components <c,-2c,c>. So is this saying that since you can describe vector A with just a single variable (c) that is is described by a line?

Homework Statement The vectors that are perpendicular to (1,1,1) and (1,2,3) lie on a ____. Homework Equations The Attempt at a Solution This is really straight forward, but I cannot validate the answer to myself. The textbook says that they should lie on a line, but why is this? Obviously...

Hi everybody, I am currently a Junior in college studying Physics. I am planning on going to Graduate School, which obviously requires the GREs. I have looked up that the physics GRE is 12% Quantum Mechanics (as per this source https://www.ets.org/gre/subject/about/content/physics). However...

Homework Statement Use either image charge method of separation of variables to solve: The distance between two large, grounded parallel conducting plates is 4x. Between them, two point charges +Q and -Q are inserted and have a distance x and 3x from one of the plates. (A line connecting the...

Homework Statement Two point charges of equal value are placed a distance 2b from one another. In the middle, there is a grounded conducting sphere. What is the minimum radius of the sphere required to cancel out the repelling force between the two charges? (Solve using Image Charge Method)...

Homework Statement This problem is very easy, but I'm not sure how best to "prove" it. This part of the question just states: Prove that (1/z)* = 1/(z*) where z* is the complex conjugate of z. Homework Equations The Attempt at a Solution So the complex conjugate of z = x + iy is defined...

Nevermind, sorry.. Apparently I forgot to type ".txt" at the end..

Homework Statement This isn't really for homework, but I wasn't sure where else to put it. anyone wishes to move it, that is fine. I'm just getting into some research and I was tasked with reading data from a text file into MatLab and then graphing it by fitting it with exponentials. I am very...

Sorry, I thought I could be more a little more explicit about my response at the bottom. Since Euler Approximations go off of the slope of the tangent line of the exact solution and as t is increasing, the slope of the tangent line of the solution approaches 0, so the error should be approaching...

Homework Statement y'' + 4y' + 4y = 0 ---- y(0) = 1, y'(0) = 5 Find the exact solution of the differential equation. Use the exact solution and Euler's Method to compute Euler's Approximation for time t = 0 to t = 5 using a step h=0.05. Plot Euler's & Exact vs. t and plot Error vs. t. Then...

Homework Statement Write down the equation of motion for the downward journey of a baseball subject to quadratic drag. Find v as a function of y and, given that the downward journey starts at ymax (given below), show that the speed when the ball returns to the ground is: vterv0 /...

Got it! Thanks for all of the help! It ended up working out when I fixed the sign issue so that the differential equation represents the upward motion rather than the downward motion. Thank you for all of your help!

Ok, that makes sense, but I am a little confused as to how to create another differential equation for the downward equation. Would I just flip the sign and make it -mg-cv 2 ? The only thing I can think of is to make g negative and keep cv 2 negative since drag always opposes motion. Is that...

Homework Statement A projectile that is subject to quadratic air resistance is thrown vertically up with initial speed v0. (a): Write down the equation of motion for the upward motion and solve it to give v as a function of t. (b): Show that the time to reach th top of the trajectory...

I have been learning some introductory quantum mechanics and stimulated Emission is giving me some problems conceptually. I understand that photons can be absorbed to bump electrons up to higher energy levels and that electrons in the higher energy state spontaneously decay back to the lower...

In my theoretical mechanics class, we went over some very basic conservation laws (namely momentum) and talked about colliding masses. Say you have 2 masses, m1 and m2. m1 is moving to the right (towards m2) with velocity v. m2 is stationary. After the two masses collide, m1 recoils with...

That's what I thought, thanks. So I have reduced it as far as I can, and it is obvious that you still cannot solve, so would an appropriate answer just be that there are No Solutions?

Homework Statement I am in a calculus class where we are learning the introduction to row reduction. I have done this before in other courses, so I am familiar with the process, but I am not sure about this one. We were given: x4 + 2x5- x6 = 2 x1 + 2x2 + x5 -x6 = 0 x1 + 2x2 + 2x3 - x5 +...

Homework Statement Silver has a density of 10.5E3 kg/m3 and a resistivity of 1.6E-8 Ω*m at room temperature. On the basis of the classical free electron gas model, and assuming that each silver atom contributes one electron to the electron gas, calculate the average time, Tau, between...

Homework Statement (a) Find the Fourier transform f(ω) of: f(x) = cos(x) between -pi/2 and pi/2 (b) Find the Fourier transform g(ω) of: g(x) = sin(x) between = -pi/2 and pi/2 (c) Without doing any integration, determine f(ω)/g(ω) and explain why it is so Homework Equations f(ω) =...

I am pretty confused. The only thing jumping out to me on what to do is to substitute substitute (f*g)(x) = integral from -pi to pi of (f(y)g(x-y))dy into the integral for en and work it like a double integral. I am not exactly too sure if this would work though because I cannot think of where...

Homework Statement (f*g)(x) = integral from -pi to pi of (f(y)g(x-y))dy f(x) = ∑cneinx g(x) = ∑dneinx en is defined as the Fourier Coefficients for (f*g) {the convolution} an is denoted by: en = 1/(2pi) integral from -pi to pi of (f*g)e-inx dx Evaluate en in terms of cn and dn...

edit: the integral should be read as follows: the bounds on the first integral go from 0 to pi quarters. The bounds on the second integral go from 0 to 1. The bounds on the third and final integral go from 0 to sqrt(1-r2cos2(theta))

A classmate of mine showed me the integral that they set up to solve the problem to get the result of 8(2-sqrt(2)) but I cannot quite figure out why. They set up a triple integral as follows: 16 0∫π/40∫10∫(sqrt(1-r^2cos^(θ))) [r] dzdrdθ Any ideas where this comes from?