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...
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...
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"...
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]...
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...
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?
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 -...
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...
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...
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?
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...
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)...
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.
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?
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...
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...
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?
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?
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...
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)...
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...
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...
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...
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?
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...
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...
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...
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...
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...
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...
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!
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...
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...
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...
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?