Recent content by ranytawfik

Now my problem with your formulation of \Psi is the following: In Pauli-Schrödinger equation, there is coupling between \psi\uparrow and \psi\downarrow that occurs in the differential equation due to the Pauli's matrices. And this is captured through using \Psi on a form of vector. In the...

Hi rigetFrog, If the magnetic field is very strong, then (as you stated) it’s going to be straight forward (simply one fermion per 1, 2, and 3). If the magnetic field is weak, you don’t have to have an opposing confining potential to have mixed spins. The magnetic interaction between the...

Thanks Dr Claude. Your answer make sense and consistent with my understanding. I'm assuming the same concept can be applied if we have more than 2 fermions (3 for example)? We have to list all the scenarios, assign correct symmetricity, and finally linearly combine the resulting wavefunctions.

When solving Pauil-Schrödinger Equation for 3-fermions in a potential well and a magnetic field, we basically solve the vector, \Psi(r_{1},r_{2},r_{3})=\left( \begin{array}{cc} \psi\uparrow(r_{1},r_{2},r_{3}) \\ \psi\downarrow(r_{1},r_{2},r_{3}) \end{array} \right) The...

Hi, Assume I’m solving a 2-particle (fermions) problem in a potential well. If I set the wavefunction as anti-symmetric, then by default I’m assuming that the two particles has the same spin and hence exchange interaction has to be accommodated for. But what if the 2 fermions have different...

Thanks strangerep and Bill. I'll try to do what you suggested, Bill, and post a follow up with the detailed Latex equations and procedures.

Check: http://en.wikipedia.org/wiki/Hyperfine_structure#Magnetic_dipole It has an expression for the magnetic coupling between an electron the nuclei but the same expression is also used for electron-electron magnetic coupling.

Problem: ----------- I’m trying to understand how to generally find Eigen functions/values (either analytically or numerically) for Hamiltonian with creation/annihilation operators in many-body problems. Procedures: -------------- 1. I setup a simple case of finite-potential well...

Lucy, Try to google “table for high symmetry points for brillouin zone” and you should get several web sites that contains table for the coordinates of the high symmetry points for several types of crystals. Rany

Thanks Eugene for the welcome and the reply. Equal thanks to ytuab. Eugene, I was trying to avoid Breit equation due to several reasons: 1. The exhaustive computations due to its 4N spinors. The only solution to this issue is to use pseudo-potential approach and just freeze the core...

Can Dirac equation be used for many particles (fermions) system (i.e. a nucleus with many electrons)? And in this case how do you incorporate the anti-symmetry nature of the wavefunctions? Obviously Slater determined will complicate the equation to a point where it’s almost impossible to solve...