Recent content by per.sundqvist

Hunds rules are empirically based and turns out to be true for almost cases, but in general they cannot be proven, and as well there are counter examples. I see you have 7 electrons, but what is the binding force? Nitrogen nuce? model potential of some kind? The exchange could in some rare...

What happens to the Dirac equation it self when the coordinates in it (also in derivatives) are transformed according to the Lorentz transform? I was told, but never checked it, that Diracs equation is invariant under such transform, but it semes you think not. My tip: Do the transform in 1D and...

cos(x)=1-x^2/2!+x^4/4!-... \delta E\propto<\Psi_0\mid x^4\mid\Psi_0>

Even though the spin was investigated non-relativistic before Dirac, it doesn't mean that it is not relativistic. First came the experiment, later a model by Pauli, then Dirac explains its origin, from relativity theory. As I pointed out in #9, the spin is more like a magnetic dipole. It...

That was interesting to read, but it sounds almost to good to be true...? The Hamiltonian was also like mv^2/2, so my question is: Why didn't Dirac use this instead? There must be some problem with this, with some extra condition, or?

I can't read your equation, but it seems its missing a square root. From my knowledge the relativistic Lagrangian is given by (1D for simplicity): L=m_0c^2\sqrt{1-\left(\frac{\dot{x}(t)}{c}\right)^2}+q\vec{A}\cdot\dot{\vec{x}}-q\Phi(x) I remember I learned to derive the Schrödinger...

You could think about it rather as an intrinsic magnetic dipole m. Classically this could be calculated for a circular loop with current I, enclosing an area A, as: m=I*A, where A=pi*r^2. But here (for the electron) we don't know either the current I or the radius r. In the limit r->0 we could...

It becomes even more complicated when you consider more electrons in a magnetic field! You would need to fix (i.e., minimize) some constant terms in each A for each electron in order to obtain the global minimum of the quantum many-electron system.

Hmm sorry, I meant that a single slater determinant does not necessary preserve the total spin eigenstate, but that you can obtain such if you take a proper linear combination of the slater determinants (alpha, beta spinor functions). Generally you don't need Slater determinants to obtain...

If it is expressed in product form of orbitals, a general anti-symmetric wave function could be written as a linear combination of slater determinants. This will normally mess up the total spin of the particles, but you get anti-symmetry which is good. For N particles you have 2^N spinor...

Where have you got this from? The only way you could coupe the spinor components in a double slit (which is non-magnetic) is by the spin-orbit interaction. \hat {H}_{so}\propto (\vec{E}\times\vec{p})\cdot\vec{\sigma} acting on the spinor: \vec{\Psi}=(\Psi_{\uparrow},\Psi_{\downarrow})^T...

You could also consider cases where particles are not bound perfectly, but within a finite barrier. In such case you could find so called meta stable eigen states, which have imaginary components. The Hamiltonian is Hermitian though, but the boundary conditions are wave like at the boundary...

Numerically you could use pdetool within MATLAB (type: pdetool at the MATLAB prompt), where you could solve this eigen value problem in 2D (Its not that you know or could specify k1, you will get it from the numeric solution). Other better program is COMSOL multiphysics. This problem looks...

Firstly they can annihilate because it is possible. Secondly, it is short lived since it is the overlap of their wave functions that determines the lifetime. Separate them enough and they will never annihilate. Or delay the time by applying a strong electric field, causing polarization, and...

Here the planet or sun have a huge mass comparable to the object (photon). I can think of an experiment where you have a gamma-ray photon package (Gaussian like blob), like 1Gev which is hitted closely by a photon of visible light 1eV. Would that photon bend in presence of the other? If yes ->...