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  1. U

    Dispersive Component of Surface Energy

    Bump, I still don't know what constitutes the Dispersive Component of Surface Energy.
  2. U

    Dispersive Component of Surface Energy

    Can anyone tell me what the definition of Dispersive Component is?
  3. U

    Dispersive Component of Surface Energy

    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...
  4. U

    Particle Flux Derivation

    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...
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    Particle Flux Derivation

    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...
  6. U

    Complaint Why Is Noone Answering My Question?

    I check back every hour and my topic has 180 views but no replies from experts. Why?
  7. U

    Particle Flux Derivation

    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.
  8. U

    Particle Flux Derivation

    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...
  9. U

    Particle Flux Derivation

    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...
  10. U

    QM - Spin operator conjugate question

    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.
  11. U

    Derive E field for a disk

    Learn how to use Coulombs Law. That will give the exact result for the E field of a disk of charge.
  12. U

    Variational Method - Gaussian Trial Wavefucntion

    Any ideas guys? It's the gaussian that's irritating me. How do I integrate it?
  13. U

    Variational Method - Gaussian Trial Wavefucntion

    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...
  14. U

    Normalised Energy Eigenfunction (Probability with Dirac Notation)

    How do I integrate e^[(-1/2)x^2] dx from -∞ to ∞ ?
  15. U

    LaTeX Latex: is it possible to install something to mirror microsoft word equation editor

    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 :(
  16. U

    Normalised Energy Eigenfunction (Probability with Dirac Notation)

    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...
  17. U

    Hermitian Operator in Inner Product

    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...
  18. U

    Normalised Energy Eigenfunction (Probability with Dirac Notation)

    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?
  19. U

    Hermitian Operator in Inner Product

    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.
  20. U

    LaTeX Latex: is it possible to install something to mirror microsoft word equation editor

    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...
  21. U

    Hermitian Operator in Inner Product

    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} >...
  22. U

    Normalised Energy Eigenfunction (Probability with Dirac Notation)

    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)...
  23. U

    Hermitian Operator in Inner Product

    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...
  24. U

    Mechanics: Coordinate systems and vector's

    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...
  25. U

    Mechanics: Coordinate systems and vector's

    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.
  26. U

    Mechanics: Coordinate systems and vector's

    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} +...
  27. U

    Vector Calculus: Integral Theorems

    Don't worry I got it.
  28. U

    Vector Calculus: Integral Theorems

    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...
  29. U

    Relativistic Kinematics

    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.
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