The Fock space is an algebraic system used in quantum mechanics to describe quantum states with a variable or unknown number of particles. It is named after V. A. Fock.
Technically, the Fock space is the Hilbert space made from the direct sum of tensor products of single-particle Hilbert spaces:
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— Wikipedia on Fock space
2009.12.04 Friday ACHK
Neutrinos could also be used for studying quantum gravity effects. Because they are not affected by either the strong interaction or electromagnetism (unless they have a magnetic moment), and because they are not normally found in composite particles (unlike quarks) or prone to near instantaneous decay (like many other standard model particles) it might be possible to isolate and measure gravitational effects on neutrinos at a quantum level.
— Wikipedia on Neutrinos
2009.12.03 Thursday ACHK
In fact, the spectrum of interpretations in quantum mechanics has a close analogue in probability theory.
Note that anyone who acted that way would be silly, and that their error would have little to do with QUANTUM MECHANICS, but mainly with PROBABILITY THEORY. Probability theory is the special case of quantum mechanics in which ones algebra of observables is commutative. (This becomes a theorem in the context of C*-algebra theory.) Quantum mechanics has special features due to the noncommutativity, but probability theory already exhibits certain subtleties of interpretation, which I believe are a large part of what’s at stake here.
— John C. Baez
2009.12.02 Wednesday ACHK
Since in some sense the interaction picture can be thought of
as rotating with the system ket
only that part of the electromagnetic wave that approximately co-rotates is kept;
the counter-rotating component is discarded.
— Wikipedia on Rotational Wave Approximation
2009.12.01 Tuesday ACHK
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
The development of an accurate mass formula is one of several fundamental aspects to developing a working theory of everything, which can overcome the incompatibilities between current classical and quantum physics theories.
— Wikipedia
2009.11.06 Friday ACHK
In condensed matter physics, the spin–charge separation is an unusual behavior of electrons in some materials under some special conditions that allows the electrons to behave as a bound state of two independent particles, the spinon and the holon.
— Wikipedia on Spin–charge separation
2009.10.31 Saturday ACHK
Finally by using a Wick rotation one can show that the Euclidean quantum field theory in (D + 1)-dimensional spacetime is nothing but quantum statistical mechanics in D-dimensional space.
— Wikipedia on Imaginary Time
2009.10.27 Tuesday (c) ACHK
Computational Physics does not mean “numerical”!
— Prof. Hai-Qing Lin
2009.10.24 Friday (c) ACHK
In physics, the scattering matrix (or S-matrix) relates the initial state and the final state for an interaction of particles.
— Wikipedia on S-matrix
2009.10.18 Sunday (c) ACHK
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In 1895, in his novel, The Time Machine, H.G. Wells wrote, “There is no difference between time and any of the three dimensions of space except that our consciousness moves along it.” He added, “Scientific people … know very well that time is only a kind of space.”
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— Wikipedia
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2009.03.12 Thursday
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Particles are localized bundles of energy and momentum.
A wave, in contrast, is a disturbance spread over spave.
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— p.107 Principles of Quantum Mechanics, by R. Shankar
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2008.12.20 Saturday
Physics Town 