# Search results for query: *

1. ### Single Slit Details

Hello! I am looking for resources to give me details of the single slit experiment. I want to code a simulation of the experiment, but most information i find is too simple or missing details. I need equations for the two angles of the particle (angle with respect to x direction and angle with...
2. ### Heisenberg's Microscope Derive Exactly Uncertainty Principle

Thank you so much vangees71! That was a great answer. However, I am trying to find an experiment (even a thought experiment) that challenges the extreme limit of the Heisenberg's uncertainty principle (where you do obtain hbar over 2). The double slit experiment is an excellent demonstration...
3. ### Heisenberg's Microscope Derive Exactly Uncertainty Principle

Can the Heisenberg's Gamma Ray Microscope thought experiment derive the Uncertainty Principle precisely? Most derivations I find, the uncertainty is roughly 2h, whereas the uncertainty principle is "hbar over 2". Is there anywhere where there is more precise calculations to obtain "hbar over 2"...
4. ### Rotation and Boost Commutating on the Same Axis

I want to prove that: [J_1,G_1] = 0 Where J is the rotation operator and G is the boost operator (subscript refers to the axis). I am using the Jacobi identity: [[J_1,J_2],G_3] = [[G_3,J_2],J_1] +[[J_1,G_3],J_2] Using other identities, I got: [J_3,G_3] = [G_2,J_2] - [G_1,J_1]...
5. ### Radial Velocity of the centre of mass of spectroscopic binary system

My book says (Foundations of Astrophysics): " The radial velocity ... can be found from the Doppler shift of the star's absorption lines: \nu_{r}=\frac{\Delta\lambda}{\lambda}c If the star you are observing is part of a spectroscopic binary system, you can separate the radial velocity of...
6. ### What should I write for my curriculum vitae?

Ok, that's sounds like a plan, thank you so much for the great advice!
7. ### What should I write for my curriculum vitae?

I am currently in my 3rd year of physics and I wanted to do some research with a professor. I have emailed him and he said that I need to provide him with a transcript and a cv. But I have no experience doing research at all. So what do I include in the cv?
8. ### Singular behavior of the density state called a van Hove singularity

Homework Statement I was doing a condensed matter problem (3rd year) of a phonon dispersion relation for a monatomic linear chain. It asked told me to derive an expression for the density state per unit length and I obtained the following: g(\omega) = \frac{L}{a\p} \frac{1}{4C/M -...
9. ### Schools Graduate School Mathematics Preperation

These are great suggestions! Exactly what I was looking for. Thanks so much for your awesome replies!
10. ### Schools Graduate School Mathematics Preperation

Here is my situation: I am currently finishing my undergraduate physics program and thinking of doing graduate studies. My only concern is that the knowledge of mathematics is fairly weak. My program offers little mathematics, its very general physica. I am interested in doing theoretical...
11. ### Dimensionality of Phase Space

Ok, so if I look at the molecule as two points (since there is two atoms per molecule) connected by a spring, each point has 6 coordinates that describe it. The coordinates being, say, x, y, z, θ, ∅ and d (the length of the spring). Now, since there is 2 points in our system, we have x1, x2, y1...
12. ### Dimensionality of Phase Space

so each molecule has two atoms, each atom has 6 degrees of freedom, thus the system has 12 degrees of freedom and since there is N molecules, the dimensionality is 12N?
13. ### Dimensionality of Phase Space

Homework Statement A classical gas consists of N molecules; each molecule is composed of two atoms connected by a spring. Identify the dimensionality of the phase space that can be used to describe a microstate of the system. The Attempt at a Solution I believe the answer is 12, but...
14. ### Variational Principle of 3D symmetric harmonic oscillator

<V> does not have units of energy... But thank you for showing me the integration, I did not use dV, which will cause many problems... thanks!
15. ### Variational Principle of 3D symmetric harmonic oscillator

Homework Statement Use the following trial function: \Psi=e^{-(\alpha)r} to estimate the ground state energy of the central potential: V(r)=(\frac{1}{2})m(\omega^{2})r^{2} The Attempt at a Solution Normalizing the trial wave function (separating the radial and spherical part)...
16. ### Orthogonality and Weighting Function of Sturm-Liouville Equation

Ok, so looking at the equation: (\lambda_{m}-\lambda_{n})\int(f(x))y'_{n}y'_{m}=0 the only possibility is f(x)=0 because no matter what I do, I can't get terms to separate and moved to the right hand side.
17. ### Orthogonality and Weighting Function of Sturm-Liouville Equation

I don't quiet understand what it means then to show if the derivatives are orthogonal...
18. ### Orthogonality and Weighting Function of Sturm-Liouville Equation

Sorry about that... Anyway, well I found a way to prove orthogonality and ended up with: (\lambda_{m}-\lambda_{n})\int(w*y_{n}*y_{m}) =0 (integral from a to b) Now how do I find the weighting function?
19. ### Orthogonality and Weighting Function of Sturm-Liouville Equation

Homework Statement A set of eigenfunctions yn(x) satisfies the following Sturm-Liouville equation: \frac{d(f(x)*y'_{m})}{dx}+\lambda*\omega*y_{m}=0 with following boundary conditions: \alpha_{1}y+\beta_{1}y'=0 at x=a \alpha_{2}y+\beta_{2}y'=0 at x=b Show that the derivatives un(x)=y'n(x) are...
20. ### Sturm-Liouville theory applied to solve Helmholtz equation

When k=0, the general solution is: y(x)=Ax+B. First boundary condition says y(0)=0=B, thus B=0, and y'(L)=0=A, thus A=0. So k=0 is not an eigenvalue.
21. ### Sturm-Liouville theory applied to solve Helmholtz equation

ok, so the solution to y''=0, y(0)=0 and y'(L)=0 is that either y=0 or y=C (some constant)
22. ### Sturm-Liouville theory applied to solve Helmholtz equation

Is this Laplace's equation? We haven't seen how to solve it yet... Can you help me? I've searched the internet and it shows plenty of ways to solve it in different coordinate systems, not really sure what to do with it...
23. ### Sturm-Liouville theory applied to solve Helmholtz equation

so when k is zero, we know that y'(L)=0 and y''(x)=0, thus y=C , which is another constant?
24. ### Sturm-Liouville theory applied to solve Helmholtz equation

Thanks a lot for the help! You guys are great! One more thing, when you say to check the equation when k=0, you mean use the general equation (knowing A=0) and say that y=B is a solution?
25. ### Sturm-Liouville theory applied to solve Helmholtz equation

Ok, so to avoid trivial solutions, we can say that: k=\frac{pi}{2L} , k=\frac{3pi}{2L} Within the range of [0,2*pi]. But how is knowing a value of k going to help find the eigenfunctions? If the values of k are the eigenvalues, how do I use them to find the eigenfunctions?
26. ### Sturm-Liouville theory applied to solve Helmholtz equation

Homework Statement Find the eigenfunctions of the Helmholtz equation: \frac{d^2y}{dx^2}+k^2y = 0 with boundary conditions: y(0)=0 y'(L)=0 Homework Equations General Solution: y = Asin(kx) + Bcos(kx) The Attempt at a Solution I found that at y(0) that B=0 and that...
27. ### Energy Levels According To Second-Order Perturbation Theory

Homework Statement If E1≠E2≠E3, what are the new energy levels according to the second-order perturbation theory? Homework Equations H' = α(0 1 0) (1 0 1) (0 1 0) ψ1= (1) (0) (0) ψ2= (0)...
28. ### Eigenstate for a 3D harmonic oscillator

Homework Statement A 3D harmonic oscillator has the following potential: V(x,y,z) = \frac{1}{2}m( \varpi_{x}^2x^2 + \varpi_{y}^2y^2 + \varpi_{z}^2z^2) Find the energy eigenstates and energy eigenvalues for this system. The Attempt at a Solution I found the energy eigenvalue to...
29. ### Finding energy eigenvalue of a harmonic oscillator using a Hamiltonian

Good point! I can also do it that way, I'll try it out. This problem involves a 2D harmonic oscillator (which the Hamiltonian was for x). To find the degeneracy of the first excited state, can I state that since ωx=ωy=ω, that n = nx + ny. Then I can write ny=n - x, and set up the following...
30. ### Finding energy eigenvalue of a harmonic oscillator using a Hamiltonian

We haven't done any sort of Gaussian... But I came up with another way to solve, can you see if this makes sense: I can write the Hamiltonian as: H =\frac{p^2}{2m} + x^2 (\frac{m\varpi^2}{2} + \frac{\lambda}{\sqrt{2}}) or H = \frac{p^2}{2m} + \frac{mω'^2x^2}{2} where...
31. ### Finding energy eigenvalue of a harmonic oscillator using a Hamiltonian

Ok, so now I tried to perform the differential equation, but then I get an equation in the form of: Ψ=Ae(ς-E)x+Be(-(ς-E)x) How can I find the energy eigenvalue from this equation?
32. ### Finding energy eigenvalue of a harmonic oscillator using a Hamiltonian

Homework Statement Find the energy eigenvalue. Homework Equations H = (p^2)/2m + 1/2m(w^2)(x^2) + λ(x^2) Hψ=Eψ The Attempt at a Solution So this is what I got so far: ((-h/2m)(∂^2/∂x^2)+(m(w^2)/2 - λ)(x^2))ψ=Eψ I'm not sure if I should solve this using a differential...
33. ### Simplification of Dirac Notation

How would you simplify this expression: <a|<b|a>|a> where ψ = |a>|b> and I'm finding ψ*ψ.
34. ### Electrostatic energy of two opposite charges in water and in a vacuum

Ok that makes sense, so D is dialectric constant and let's say r now is the distance, which is missing in the equations.
35. ### Electrostatic energy of two opposite charges in water and in a vacuum

I did do that, D=80 for water and D=1 for a vacuum
36. ### Why doesn't oil and water mix?

I found it for water molecules around a hydrophobic molecule when multiplicity is reduced from 6 to 3
37. ### Electrostatic energy of two opposite charges in water and in a vacuum

So, for water: E=\lambdaKT/80? And for a vacuum: \lambdaKT?
38. ### Electrostatic energy of two opposite charges in water and in a vacuum

Homework Statement Compare the electrostatic energy of two opposite charges e and -e, a distance 7 angstroms apart in water at room temperature and that in vacuum (express the energy in terms of Bjerrum length) Homework Equations E = 1/(4(p\pi\epsilonD)*(-e^2)/r^2 ? The Attempt at a...
39. ### Making a eigenvector a linear combination of other eigenvectors

Ok, that makes sense, thanks a lot!
40. ### Why doesn't oil and water mix?

Homework Statement Explain why water and oil doesn't mix at room temperature using the entropy and free energy that you found to explain. Homework Equations The entropy that I found is -(Kb)ln(2) and the free energy is (Kb)(T)ln(2). The Attempt at a Solution Can someone direct me...
41. ### Making a eigenvector a linear combination of other eigenvectors

Homework Statement Write the eigenvector of \sigmax with +1 eigenvalue as a linear combination of the eigenvectors of M. Homework Equations \sigmax = (0,1),(1,0) (these are the columns) The Attempt at a Solution ... Don't know what to do. Can someone show me how to do this using...
42. ### Finding psi(x,t) using psi(x)

Homework Statement Consider the free-particle wavefunction, ψ(x)=(pi/a)^(-1/4)*exp(-ax^2/2)  Find ψ(x,t) The Attempt at a Solution The wavefunction is already normalized, so the next thing to find is coefficient expansion function (θ(k)), where: θ(k)=∫dx*ψ(x)*exp(-ikx) from...
43. ### Force applied to a mass of an inclined plane with mass

There is a box of mass m on a wedge of mass M with angle θ (the triangle also has a angle of 90 degrees). I need to find the force applied on the little mass, this is what I got: F=-mgsinθ+Mgsinθ Where the first term refers to the force of gravity applied to the mass m and the second term...
44. ### Question if expectation value is considered a measurement?

Hello, I was just curious about expectation values. One of the postulates of quantum mechanics state: The only possible results of a measurement is an eigenvalue of the operator. Now, is the expectation value considered a measurement, thus considered an eigenvalue? Thanks!
45. ### Velocity change by force in one and two inertial frame confusion

The velocity is equal to the force multiplied by the time. When you take the integral of the velocity with respect to time, you get the force times the time squared. Now, for the second inertial frame velocity, I do not understand where he gets the equation (V(2t)). I think he means to...
46. ### Velocity change by force in one and two inertial frame confusion

Yes, the velocity is a function of time. When a constant force is applied, the velocity changes with respect to time.
47. ### Velocity change by force in one and two inertial frame confusion

Hi, I just finished class and my professor was writing some of Newton's Laws on the board and derived some equations. We ended up with: V(Δt)=FΔt (this is for velocity in first inertial frame V(2Δt)=2FΔt (this is for velocity in second inertial frame Then he went and got the position in...
48. ### Amount of Energy to Fuse Two Atoms

Yes, that is what I was wondering about. Thank you Drakkith, that was also a very good answer, its interesting! Now, I've never taking a particle class yet, I'm just being curious! So can someone do a worked example for me: let's say you want to fuse a hydrogen atom to a sodium atom to make...
49. ### Amount of Energy to Fuse Two Atoms

Not sure... Can you describe this energy? Don't hold back on description, I'm in my third year university physics, so the more complex the better!
50. ### Amount of Energy to Fuse Two Atoms

Thank you, I wasn't sure if it was as simply as E=mc2 or there was something else more to it. But I guess not! Thanks again, highly appreciate you time! Actually, I thought of something... Does it not depend on the energy required to hold the atoms together instead of the energy of rest mass?