Am 23.11.2012 08:57, schrieb Archimedes Plutonium: > Well, I had too much to eat for Thanksgiving. I saved up some special > for dinner tonight and ate too much. So looks like I will try to eat > just cereal for the next two days. I want to try to maintain my 137 > lbs weight that I had in High School, so that means some days of near > fasting. But enough of that, lets get to important things. > > I had to make a detour into the electric motor, the rotor and thanks > to Tim's responses, I am pretty sure the problem is with the > Schrodinger Equation gives inaccurate descriptions of the "s" > orbitals. The Schrodinger Equation gives spherical orbitals to the > "s", but we all know the Dirac Equation relativizes the Schrodinger > Equation. It puts the Schrodinger Equation into motion, so that the > sphere is no longer a adequate description of the "s" orbital. So what > happens when you put a sphere into motion? What figure comes out? > Well, easily that a sphere produces when in motion is a cylinder > shape. > > So the "s" orbitals of chemistry should really look like a cylinder > rather than a sphere. Now the Schrodinger Equation gets a lot of > elongated ellipses for the p, d, f orbitals. And if we put those into > the Dirac Equation, it elongates them even more so. The Dirac Equation > makes orbitals more like wire loops around the nucleus of an atom.
Thats of course not what you will find in text books.
The s=1/2, L=0, j=1/2 orbitals of hydrogen are spherical symmetric but are carrying an intrinsic spin-induced electric current (see eg. Gordon decomposition of current in Landau/Lifshitz).
What is not possible for a spherical symmetric spin 0 field - current is an effect of the field gradient - is the normal case for a vector field:
Alle the spherical symmetric charge densities carry a fixed electric current per sphere shell around an axis, resulting from the algebraic imprinted vector current. It needs no field gradient.
This is the reason why these currents and their magnetic fields are intrinsic and cannot slow down.
A ground state with vanishing current distributions does simply not exist.
Since spin and angular momentum are not distinguishable in not so symmetric cases, it is much easier to say - in a quasiclassical approximation, that for a spinor field the observable densities current density "c gammma" and local angular momentum "J = L + 1/2 sigma" never vanish.