Recent content by jiadong

A metaphor: Suppose there are two rectangle cakes. For them, everything is the same excepte the shape: the first one with side length 2 inchs and 2 inchs, the second one with side length 1.7 inchs and 2.35 inches. Now if we want to choose the bigger one and we are allowed to choose one of them...

Now I see, the equation \left (\frac{\partial \hat{\rho}}{\partial t} \right )_{\text{exp}} + \frac{1}{\mathrm{i} \hbar} [\hat{\rho},\hat{H}]=0. plays similar role in quantum statistical mechanics as the Liuville's Equation does in Statistical mechanics.

Yes.! Finally, I find that someone also define the square of FT of the velocity autocorrelation as the vibrational density of state. now I think I understand it more.

My data is simulation data. I also think the problem is in the method of FT. Thanks a lot!

Thanks, all the same. I also think the FT of the autocorrelation function should give the relative probability of different component, eg the relative probability of different vibritional density of state.Thanks, my reply is too late.

I am trying to understand the IR spectra of liquid. I can get the autocorrelation function of atoms' velocity, <v_{i}(0)v_{i}(t)> make a Fourier Transformation, the vibrational density of state (VDOS) can be obtained. Does the VDOS always be positive? Or it can also take negative value...

Hi, What I know is that : Just like a rotation is 3-D space, Lorentz transformation is a rotation in 4-D space-time.

Thank you, Kith! You mean that if [H,ρ]=0,thenthe eigenvectors of the ρ are the constituents of a incoherent mixture.

But the expression \hat{\rho}=\Sigma_i \lambda_i |E_i\rangle\langle E_i| is of the same form to the defination of desity operator in a mixture state. I still don't know the specail characteristics of thie kind of rho. I am sorry, I am so stupid to understand the physical mean of [H, ρ ]=0...

If ρ is the desity operator of a ensemble. We get (ih/2π) ∂ρ/∂ t = [H,ρ ]. for a stationary state [H,ρ ]=0 . So H and ρ can share the same eigenvectors. Can someone explain what does this mean? :smile:

Great! The solutions of an aquation may have less symmetry than the equation.

Exchange integrals indeed come from the Identical Principal, which is occur only in Quantum world. For example, for electrons you can find that the exchange integrals comes from the Pauli exclusion principle. The total wave function (|fai> ) should be antisymmetric, and it should have a...