Recent content by Ratpigeon

Homework Statement How does the state of a particle in an ISW evolve with time after the width of the well doubles - from a to 2a If the particle starts in the ground state of the half width well, then immediately after the well doubles it will be undisturbed therefore the initial wave...

Thanks - I probably should have known that, I was just put out when my plot of the chaotic-ness of a system turned out to be... chaotic. ;P

I'd done all the linearising stuff - I found my problem; I needed to use a Jacobean matrix, instead of just a system

Homework Statement I'm working on an assignment about the chaotic behaviour of the Duffing Oscillator, using Wolfram Mathematica, which has a package that can be used to calculate Lyapunov exponents. From looking the oscillator up online, I have a set of parameters that result in...

Homework Statement I am trying to show that for a duffing oscillator described by x''+2g x'+ax+bx^3=0 with a<0, b>0 the equilibria at x=+- \sqrt{-a/b} are stable Homework Equations I used coupled equations, and the characteristic equation of a linear system The Attempt at a Solution...

Homework Statement Show that for a particle in a central potential; V=f(|r|) H is conserved. Homework Equations THe hamiltonian is H=\sum(piq'i)-L It is conserved if dH/dt=0 Euler-Lagrange equation d/dt(dL/dq')=dL/dq Noether's Theorem For a continuous transformation, T such...

Homework Statement Derive an expression for the Fresnel Zone Plate's focal length Homework Equations The fresnel zone plate has a transmittance function 1/2 (1+cos (ar^2)circ(r/2l)The Attempt at a Solution Using Eulers formula. this splits into e^(iar^2)+e^(-iar^2) Since the transmittance...

Homework Statement Show that if I and J are ideals of the (commutative) ring; R then S={xy|x in I y in J} is not necessarily an ideal but the set of finite sums IJ={Ʃ(xvyv)|xvin I yvin J} is (and called the product ideal). Homework Equations An ideal satisfies the properties For...

Thanks thatreally helped. i got it out now

Homework Statement Integrate from zero to infinity; f(x)=\sqrt(x)log(x)/(x^2+1) Homework Equations Branch cut makes log(z)= ln|z|+i Arg(z) Poles are at +/- i and Res(z=i) is \pi/4 e^(i \pi/4) I'll need to close the contour; probably as an annullus in the top half of the...

Right - got them. I got my brain stuck on taylor series, when I needed L'hopitals rule. Thanks. They're simple poles with limits z->z_0=z_0, right? :)

Homework Statement Find the order of the poles of f(z)=z/(e^z-1) Homework Equations The poles are at z=2 π i k k\inZ\0 (Because at z=0 f(z) has a removable singularity -set f(0)=1) The Attempt at a Solution I tried using the Taylor series of e^z - \sumz^n/n! But I just...

Homework Statement Given the dihedral group of symmetries of a square; what is the stabiliser group of a vertex (or edge)? Homework Equations The stabiliser group is G_x={g\inG|gx=x} I guess for a vertex/edge that means the transformations in D4 (generated by reflection in x-axis and...

For part (i) - you are right, For part (ii) you have used s_x instead of V_x to determine V_y For part (iii) - yes, the acceleration is constant, but it is not equal to C; but maybe try determining the total acceleration, and the acceleration in the x direction instead of differentiating...

For part (b) you should use the equation PE=mgh (where m is the mass of the object, g is the gravitational force on the object, and h is the height of the object) You know what the initial kinetic energy is, and that at the peak of the throw; the potential energy will be equal to the the...