Recent content by sokrates

To me it looks like all he did was to sum up/down electrons for a spin-free system. Looks valid if you are interested in "pure" charge density and want to forget about spin. Nothing wrong with it.

Yes - you are right.This was exactly what I was looking for.

This is NOT homework. I am trying to solve a generalized circuit ( each node is a 4-component generalization) and matrices are 4x4 tensors. And I am trying to write them down -- making common nodes "zero" current, ending up with a matrix as in what's shown in the link...

Yes, I got it ... Just write it out explicitly and choose A,B,C,D accordingly to get the random 2N by 2N matrix. Many thanks for directing me to that.

Yes - I can do the 2x2 proof I guess. Because any 2x2 Hermitian matrix can be written as: H=\begin{bmatrix} a & c -i \ d \\ c + i \ d & b \end{bmatrix} where a,b,c,d are all real numbers. Then H can be uniquely defined in terms of Pauli matrices: \frac{1}{2}\left[ (a+b) \ I_{2\times...

No - B is the best answer because Force is defined as the net rate of change of momentum. \sum_i \vec{F_i}=0 = \frac{d \vec{\ p}}{dt} However, the momentum being constant does not mean that the speed has to be the same, nor the Energy to be the same. Mathematically you can see it like...

I posted this question over at the QM page, https://www.physicsforums.com/showthread.php?t=714076 but I realized I am really looking for a hard Mathematical proof ... A description of a numerical way of proving this would also be very helpful for me. or a reference covering the...

Hi , Thank you for the responses ... However, I still don't understand it from a matrix point of view. Let's take N = 2 , and have a 4x4 H matrix ... can one prove that my representation will always cover the full space ? I didn't follow it from the Dirac notation, Many thanks for responses.

Hi, Wasn't sure if I should post this to Linear Algebra or here. My question is really simple: Can a 2N by 2N random, and Hermitian Matrix ( Hamiltonian ) be always written as: H = A \otimes I_{2\times 2} + B \otimes \sigma_x + C \otimes \sigma_y + D \otimes \sigma_z where A,B,C,D are all...

In 2D- as you correctly pointed out the error is proportional to kf^2 ... But N is the electron number as you point out. in 2D at low temperatures kf = sqrt ( 2 pi N ) that is kf ^ 2 is proportional to Electron Density ... Then the error indeed goes as 1/N.

Pick a practical PDE, like one of those already suggested ( say, Poisson Equation in 2D) and try to solve it numerically. Yes, numerical attempt will be like designing an experiment and you will learn a lot along the way. Once you solve it numerically, in order to make sure you did...

Seebeck coefficient is a function of energy; just like conductivity. Therefore when you want the total Seebeck coefficient, it has to be weighted by their energy dependent conductivities.

This could be helpful: Specifically: Kronig-Penney Model http://en.wikipedia.org/wiki/Particle_in_a_one-dimensional_lattice

Fredrik, I agree with you %99 percent. No question. Whether or not we can measure S^2 , we can discuss separately. I can think of, admitedly hypothetical, spin-functional devices to do the deed but that's another point. I think I have to agree that I was too dismissive, theories certainly...

Yeah I think I have made my point. I do research professionally, so I don't worry about accuracy when I post on PF in my free time. To tell beginners that to understand spin, they need to dig their heads in a physics book is far from inaccurate, it's very misleading. The term "spin" can be...