Hello, I'm doing an MSc project concerned with the treatment of plastic polymers with an μ-APPJ. I have been getting a tonne of results on different plastics using an APPJ of He carrier gas with an Oxygen admixture of 1/2, 1 & 2%.
However, in my analysis I'm unsure of what the dispersive...
Yeah but how do I show it?
I know the particles can exit the cross-section through a solid angle Ω = 2π(1-cosθ), but ingrating over this angle gives me π/4nv.
I think I am doing it completely wrong but I honestly don't know how to approach this problem any other way. Taking velocity...
Hello,
It is a finite cylinder of lets say length vdt, with a cross-sectional area A of 1cm^2
The particle 'source' is a simple 3D gas with maxwellian velocity distribution (which I have already accounted for). The gas particles bounce elastically off of the walls until they exit through...
I keep getting a factor of π/2 in my answer.
So I end up getting π/4nv which is wrong. Surely someone on this forum knows how to do this? I can't find any helpful sources on the internet, yet everyone quotes it religiously when the subject of particle flux comes up.
I understand that about 1/2 the particles go in opposite directions, so for one end of the cylinder you already have 1/2nv.. But you have to take into account the angular distribution of particles with a velocity distribution [v, v + dv] coming out of the end.
And this is where the solid angle...
Homework Statement
Consider a cylindrical vessel with cross-sectional area 1m^2
Derive the particle flux (1/4n\bar{v})
Homework Equations
I have the solid angle:
\Omega = 2π(1-cosθ)
The Attempt at a Solution
I'm assuming that the solid angle represents the full area that the particles...
Simply have the 2 x 2 matrix of Sx operate on the state v, then multiply your new 2 x 2 matrix with the conjugate of v.
And yes the conjugate of v is a transpose matrix with the i's all different.
Homework Statement
Use the variational method with a gaussian trial wavefunction ψ(x) = Ae^{\frac{-a^{2}x^{2}}{2}} to prove that in 1 dimension an attractive potential of the form shown, no matter how shallow, always has at least 1 bound state.
*Figure is of a potential V(x) that has a minimum...
Do you still have it? I want to become a more active contributing member of this forum, but Latex is firmly staunching my progress :( Of course I will learn, I just don't understand why it needs to be so complicated and at certain times 'clunky' to use :(
Since both states are real, their conjugates equal their normal counterparts. So I end up using an Identity relation to superimpose the states anyway (underhanded trick from my QM lecturer :p ).
Ok so I'm multiplying and integrating over unity, hopefully a useful co-efficient should pop out...
Nicely done broslice, I assume I do the same thing for the right side?
EDIT:
Done, thanks alot, since it's hermitian, the conjugate remains the same as normal and the condition <v|\hat{A}u> = < \hat{A}v|u> is met.
Can you help me on my other topic? Just a point in what to do with the...
I squared the states to get probabilities, but now I'm left with 2 probability amplitudes that I'm stumped on how to use.
What can I use the energy for?
I know n = 0, but do I have to find the expectation value of getting the energy?
That's not what I did..
I went from \int d^{3} \vec{r} < ψ_{1}|\vec{r} > \hat{A} < \vec{r}|ψ_{2} > to < ψ_{1}|\hat{A}|ψ_{2} >
I used that identity relation with the bra of the r facing the ket of the r... it equals 1.
It takes longer to write out a question and your working, than it does to even get a reply.. And that reply either never comes or is something along the lines of 'I can't tell what you've done'.
Latex is so harsh to use, is it possible to install something to mirror microsoft word equation...
Latex takes forever to use... Well here goes:
We are supposed to assume that ψ_{1}* is a wavefunction, so we use a trick to show just that, whilst the conjugate is now something wierd
ψ_{1}* = < \vec{r}|ψ_{1} >
ψ_{1} = < ψ_{1}|\vec{r} >
So subst into
\int d^{3} \vec{r} < ψ_{1}|\vec{r} >...
Homework Statement
Normalised energy eigenfunction for ground state of a harmonic oscillator in one dimension is:
〈x|n〉=α^(1/2)/π^(1/4) exp(-□(1/2) α^2 x^2)
n = 0
α^2=mω/h
suppose now that the oscillator is prepared in the state:
〈x|ψ〉=σ^(1/2)/π^(1/4) exp(-(1/2) σ^2 x^2)...
Homework Statement
\int d^{3} \vec{r} ψ_{1} \hat{A} ψ_{2} = \int d^{3} \vec{r} ψ_{2} \hat{A}* ψ_{1}
Hermitian operator A, show that this condition is equivalent to requiring <v|\hat{A}u> = < \hat{A}v|u>
Homework Equations
I changed the definitions of ψ into their bra-ket forms...
Unsure about cartesian coordinates... I've considered the velocity of the ant in x and y directions Vx = ucos theta
Vy = usin theta
Then I considered a point on the turntable which has an angular velocity rw...
I don't know what to do now...
Ah I've done it in polar coordinates. I was half right about the addition, but I was unsure about the angular velcity of the turntable. Now doing it in cartesian.
Homework Statement
An ant walks from the inside to the outside of a rotating turntable. Write down it's velocity vector.
Use polar the cartesian coordinates.
Homework Equations
I have already derived the velocity vector in polar coordinates which is:
\hat{v} = \dot{r}\hat{r} +...
Homework Statement
Question 3 part b and c
Homework Equations
Divergence and Stokes Theorems. Knowledge of parametrization ect ect
The Attempt at a Solution
I got the B field by using curl. However any attempt to resolve the flux through the top hemisphere or even the...
Bump?
I'm sure this will take you guys under a minute when compared to the other questions here. I just want an equation or a push in the right direction thanks.