Q-reeus, you are right. I may have misunderstand it
Now I'm calculating separating minus charges and plus charges.
Also in the case that the currect i and boost v are in the same direction, the currect i is increased.
( Only puls charges are supposed to be moving. )
\rho_+ = \rho_- \qquad...
Sorry if I misunderstand you.
I don't understand why your definition of I/γ ( not Iγ ) satisfies ∂ρ/∂t + ∇.j = 0.
And your equation (3) needs to be added the current term of j, which leads to (5).
This current j term is not combatible with I/γ , I think.
And I don't see why Eq.(4) is equal...
Jno L. Thanks for your interesting comments.
This paper explains Synge's paper in 1940 about two body problem.
But as I see this paper, this method is not classical. and he used some approximations.
If we think about the effect of retardation effect correctly, we have to use a computer...
fzero, I want to know why we denied the Bohr's orbit in the point of radiating energy now.
As you know, Bohr's orbit uses the "quantization of de Broglie's wavelength", which gives the same results as Schrodinger equation.
Jano L., thanks for your reply.
But there are some points I want to...
I heard classical Maxwell equation explains why the accelerated charge radiates energy, which removed Bohr classical orbit.
But Bohr got Nobel prize for this Bohr orbit, so members of a selection committee in Nobel prize didn't understand this reason ?
When I recheck classical...
Sorry. I want to know how the next experiment (Fake of Bell inequality violation) has been thought since it was published.
Fake violation of Bell tests reinforce inportance of closing loopholes.
In the current study, the scientists showed that Eve can send strong, classical light pulses...
Many books tend to avoid explaining "what the spin actually is", I think.
But I found interesting comments about spin in the next book.
p.187 Deep down things: the breathtaking beauty of particle physics (Bruce A. Schumm)
-- So the question arises, what exactly is spin and this oddly...
Hm, I think I should have added more explanation to #11.
According to the interaction term and creation (+ annihilation) operator methods, (of course, using Feynman diagram, it is very easy to imagine), the next interactions are allowed. For example,
e^- + e^+ \to \mu^- + \mu^+
This...
The quantum field theory is originally based on Klein-Gordon, and Dirac equation.
And as we know, the electron moves unfer Lorentz force, which can be expressed as interaction term of A (= covariant derivetive).
We can not ignore this covariant derivative, which expresses Lorentz force, so...
TMSxPhyFor, I understand your idea well.
But unfortunately, the quantum mechanics (and QFT) give up reality and visualization.
First we can not visualize "spin" itself ( we only use the matrices to express spin).
See this page .
Particles (fermions) such as neutron and electron "feel" the...
I think The Story of Spin (by S.Tomonaga) explains about this "unnaturally" strong interaction between spins in detail.
Alkali metal such as sodium shows doublet spectrum.
This is caused by the quantization (up and down) of the valence electron spin 1/2 along the orbital magnetic momment l...
Sorry. I don't understand what you mean well.
Pauli exclusion principle is related to wavefunction itself (= determinant ) not Hamiltonian.
From the viewpoint of the energy, for example, the fine structure (2P3/2 and 2P1/2) is actually observed.
If only the energy of the magnetic force...
tom.stoer, What TmsxphyFor says is due to Pauli exclusion principle, I think.
Due to the first electron's spin, the second electron changes its orbit (to the higher energy level).
It is very difficult to explain from the viewpoint of the energy.
(For example, the energy level of the 2s orbit...
Even if Pauli exclusion principle exerts the "repulsive force" between particle's spin, it would not be included in the four fundamental forces, I think.
(This is due to the "mathematical" form of QFT.)
Because the four fundamental forces need to use bosons such as photon, gluon, W-boson...
The total enegies are the same in both Bohr model and Schrodinger's hydrogen.
As both satisfy the Virial theorem, 2K = - V, the average kinetic energies (K) and potential energies (V) are the same, too.
In n=1 state (1s), Bohr model electron doesn't collide with nucleus, because the angular...
Here we define unit vector n in the polar coordinate.
\vec{n} = ( \sin\theta \cos\varphi, \, \sin\theta \sin\varphi, \, \cos\theta )
Of course by 2pi rotation, this vector doesn't change,
\varphi \to \varphi + 2\pi, \qquad \vec{n} \to \vec{n}
The n component of the spinor operator is...
I think it is easier to imagine "vector" ( ex, 4-vector potential A(x) ) instead of spinor, first.
A^{\mu} (x) = ( A^0 (x), A^1 (x), A^2 (x), A^3 (x) ) \qquad x^{\mu} = (x^0, x^1, x^2, x^3)
This 4-vector A (x) means that there is a thing " vector A " at the position of x ( from the...
George Jones, I want to confirm this equation.
According to p.60 of an introduction to quantum field theorey by Peskin, Dirac field change under Lorentz transformation,
\psi (x) \quad \to \quad \ \psi' (x) = \Lambda_{1/2} \psi (\Lambda^{-1} x) \quad (S = \Lambda_{1/2}) \quad ( x' = \Lambda...
I had Sakurai's advanced qm a few month ago.
But now I don't. Sorry, I imagine from your sentence.
First, Dirac's solution includes exponential function
\psi = \int_{-\infty}^{\infty} \frac{d^3 p}{\sqrt{2E_p}} a_p u(p) e^{-ipx} \cdots
Here, both the p (momentum, energy) and x (time ...
Probably, you forget about the "magnetic energy", though the electron (charge= q ) is rotating under the magnetic field. I rearrange your equations here.
According to the Bohr model. the orbital length is an integer (n) times de Broglie's wavelength (=h/mv),
So this fact leads to your first...
According to this book (Advanced Quantum mechanics by J.J. Sakurai), the 2 upper component of Dirac spinor (4 x 1) for hydrogen atom gives very similar results to those of Schrodinger's hydrogen atom. (Of course, the angular momentums are the same, too.)
(So the "radial" boundary conditions are...
You mean that only the kinetic energy (KE) is more than 30 times the "big" rest mass energy (= mc^2) ?
According to Virial theorem, the potential energy needs to be minus 2 times the kinetic energy (V = - 2 x KE).
So the potential energy becomes minus 60 times the rest mass energy.
This means...
As far as I know, Dirac respected Einstein's special relativity.
Dirac knew about Maxwell's electromagnetic theory after knowing the special relativity according to this book.
(The Strangest Man by Graham Farmelo. )
The gamma matrix and Pauli patrix are fixed values. But their...
As far as I know, Dirac equation is equal to "special relativity".
Substituting relativistic x and t into usual accelaration equaion (of Newtorian mechanics).
Ant if we use the force F of v=0, we can get your relativistic momentum and energy.
(And the solution of Dirac equation uses four...
You say if 1 x 1 =1 and -1 x -1 = 1, it means 1 = -1 ?
This is strange.
The important point is whether wavefunction (amplitude) or wave phase exist or not.
(What you are saying is the same as Tomonaga in Story of Spin or Weisskopf, which statement are older than 1975 neutron expetiment )...
In your spin state, the spnning speed is almost light speed, and the relativistic mass is too heavy to move it.<br>
But the electron has orbital motion (kinetic energy) and orbital angular momentum, too.
If you consider the orbital kinetic energy, its speed exceeds the speed of light. ( v =...
Similar point is that the boundary conditions (radial) of Schrodinger and Dirac equations are from zero to infinity.
(Because both of them use the exponential function, which becomes zero at infinity.)
So the de Broglie's relations are applied to match this boundary condition.
Different...
I think it's one of the limits in representation by Dirac equation.
u(p) is 4 x 1 matirix (column), and \bar{u}(p) is 1 x 4 matrix (row).
To be presice, the following things are different, considering matrices ?
\bar{u}(p) u(p) = 1 \neq u(p)\bar{u}(p)
Because the former is not matrix...
Sorry . edquy99.
The "precession" of spin is widely-used, and very important.
But do you think the precession is very difficult to imagine ?
For example, you quote the Stern-Gerlach experiment, in which the direction of the spin is quantized in the external magnetic field (= z direction)...