Me 20090909:

Based on K. Young’s notes:

Action S should be defined in a way that

1. It is invariant.

2. It is additive.

3. It fulfills the experimental results.

Me 20090909:

Hamiltonian (in classical mechanics) may not be the total energy of the system.

The formal definition should be H = pv – L.

Me 20090909:

Principle of least time is the principle of least action for photon via de Broglie’s relation.

2009.11.30 Monday (c) ACHK

Planck’s constant is the quantum of action.

— Wikipedia on Action (physics)

2009.11.29 Sunday ACHK

What is the relationship between vacuum polarization and self-energy?

Vacuum polarization is the self energy of photon.

— Me@2009.11.25

2009.11.28 Saturday (c) ACHK

One of the paradoxes of quantum theory is that wave function seems to be more than just information (otherwise interference effects are hard to explain) and often less than real, since the collapse seems to take place faster-than-light and triggered by observers.

— Wikipedia on Wave function collapse

2009.11.26 Thursday ACHK

In nonlinear optics, the superposition principle no longer holds.

— Wikipedia on Nonlinear optics

2009.11.25 Wednesday ACHK

The normal distribution was first introduced by Abraham de Moivre in an article in 1733, which was reprinted in the second edition of his The Doctrine of Chances, 1738 in the context of approximating certain binomial distributions for large n.

— Wikipedia on Normal distribution

2009.11.24 Tuesday ACHK

If the electrons are cold, it is possible to show that the charge density oscillates at the plasma frequency \omega_{pe} = \sqrt{\frac{4 \pi n_e e^{2}}{m}} (cgs units) = \sqrt{\frac{n_e e^{2}}{m\varepsilon_0}} (SI units) \left[s^{-1}\right], where n_e is the density of electrons, e is the electric charge, m is the mass of the electron, and ε0 is the permittivity of free space. Note that the above formula is derived under the approximation that the ion mass is infinite. This is generally a good approximation, as the electrons are so much lighter than ions. (One must modify this expression in the case of electron-positron plasmas, often encountered in astrophysics). Since the frequency is independent of the wavelength, these oscillations have an infinite phase velocity and zero group velocity.

— Wikipedia on Plasma oscillation

2009.11.23 Monday ACHK

| \psi(t) \rangle = e^{-iEt / \hbar} | \psi(0) \rangle

Thus we see that the eigenstates of the Hamiltonian are stationary states, they only pick up an overall phase factor as they evolve with time.

— Wikipedia on Schrodinger picture

2009.11.22 Sunday ACHK