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...
1. Homework Statement
Find the Lagrangian and equations of motion for a spherical pendulum
2. Homework Equations
L=T-U and Lagrange's Equation
3. The Attempt at a Solution
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...
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...
1. 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...
1. 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...
1. 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...
1. Homework Statement
Show that if m and n are integers such that 4|m2+n2, then 4|mn
2. Homework Equations
3. 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...
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?
1. Homework Statement
The vectors that are perpendicular to (1,1,1) and (1,2,3) lie on a ____.
2. Homework Equations
3. 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...
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 here). However, how my University is set up, I will not be able to...
1. 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...