Recent content by climbon

Question about moments and torques. I understand that torque is defined as τ=Fs and understand where this comes from mathematically but am wondering why does nature make it easier to put a greater torque on an bolt with a longer lever. The only real explanation I can think of is by...

Hi, if I have a mass on a string and I swing it around my head at a constant speed, what is the resultant force on the mass (I'm looking for a qualitative rather than quantitive answer)? My inital thoughts were towards the centre of rotation, due to the tension on the string (and since the...

Thanks for your reply! I understand that now (about the corner behaving as one side of an infinitely large gap). Thanks I'm still struggling as to why lower frequencies diffract more at a fundamental level. The only reason I can think of is a rather crude explanation by relating it to momentum...

Hi, I am posting here as I can't get a satisfactory answer from google. Could anyone explain to me why low frequency sounds diffract better than high frequnecy sounds around a corner (eg the wall of a building). I understand the idea of 'wave diffracts more when opening is around the same...

Hi, I am reading a paper and can't get the same answer they do, they have; H= -i\hbar \sum_{\lambda} \int dK (a_{(k,\lambda)} g_{(1;K,\lambda)} \sigma_{1}^{+} e^{-i(\omega_{k}- \omega)t} - H.C ) Then states they do a formal integration of the Heissenberg equation for...

Hi, I am trying to work out the atomic inversion of the Jaynes cummings model using the density matrix. At the moment i have a 2x2 matrix having used the Von neumann equation (technically in Wigner function in x and y). Each of my matrix elements are 1st order pde's describing the...

I am unsure how to (mathematically) do the partial trace of a density matrix so that I can find the expectation value of an observable. I am working on a model similar to the Jaynes cummings model. My density matrix is of the form; \rho = [\rho_{11}, \rho_{12}, \rho_{21}, \rho_{22}]...

Yer its PDE class. I've tried using Charactoristics, so, \frac{\partial x(t)}{\partial s} = 2gy(t) and \frac{\partial y(t)}{\partial s} = -2gx(t) With s=t. I am not sure what to do now with regards to forming a general solution, would it be something of the form...

Hi, my equation is; \frac{\partial}{\partial t}U(x,y,t) = 2g \left( x \frac{\partial}{\partial y} - y \frac{\partial}{\partial x} \right) U(x,y,t) I want to find the general solution to this but I don't know how to find it? Any help would be great...thanks :D

I have an equation that I am trying to change the variables of, it has the form; \frac{d}{dt} W = g \frac{\partial}{\partial y} U + h x \frac{\partial^2}{\partial y^2} Z Where W, U and Z are my dependent variables (This equation is just one of 3 coupled equations but have written...

Thanks, this is my problem; H=H_{0} + H_{I} Where H_{0}= \frac{1}{2} \hbar \Omega \sigma_{z} + \hbar \omega a^{\dagger}a and H_{I}=g_{1} \sigma_{x} (a+a^{\dagger}) + g_{2} \sigma_{z} (a+a^{\dagger}) +g_{3} \sigma_{z} (a^{2} + aa^{\dagger} + a^{\dagger}a +a^{\dagger...

Hi, I am trying to solve a modified Jayne's cummings model using the Von Neumann equation and Wigner function but am having a problem with Density matrix hermicity; I am trying to solve in Schrödinger picture. I have my system Hamiltonian as; H_{0} = \frac{1}{2}\hbar \Omega \sigma_{z}...

Hi, I am trying to simplify this; x \frac{\partial}{\partial x} W(x,y) - \frac{\partial}{\partial x} (xW(x,y)) Am I correct in thinking I can do this with the product rule, as; \frac{\partial}{\partial x} (xW(x,y)) = \left( \frac{\partial x}{\partial x}\right) W(x,y) + x...

Hi, I have this equation to solve. y'' + (1/x)y' + [(x^2) + k + (m^2 / x^2)]y = 0 now, I've tried to solve this using frobenius method but cannot formulate a solution. I have that a_(n+4) = [-ka_(n+2) - a_(n)] / [n^2 +/- 2inm] is my recurrence relation, but now I'm stuck and...

I'm brushing up on squeezed coherent state and have seen them defined in terms of position and momentum squeezing and in terms of amplitude and phase squeezing...is there a relation between the two? Am i missing something obvious :p ?