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## Quantized energy - Photon

 Quote by marksesl Ok, I got it figured out. It's explained here: http://www.youtube.com/watch?v=B7pACq_xWyw In E=hv that number can only be multiplied by a whole number. So, the equation actually becomes E=nhv. For blue light, for example, the value for hv is about 3. So, only 3, 6, 9, 12 electron volts are allowed for blue light.
This is not correct. Blue light has an enery of around 3 eV, 6eV would be outside the visible par of the spectrum. Again, "quantized" does not mean that the light can only take on values that are integer multiplies of a specific number.

Your equation is the equation for e.g. multi-photon excitation of a transition in an atom.

 Ok, so a blue photon is just always 3eV. Correct? "The classical frequency of your light determines the quantization of the photons (as packets of h*nu energy). You can vary the classical frequency of your light continuously, and for every value it takes, you get a different quantized energy for your photons." So what is the classical frequency of light as opposed to the frequency contained in the photons?
 Mentor The frequency associated with the photon equals the classical frequency of the light that it corresponds to. The n=3 to n=2 transition in hydrogen produces photons with energy 1.9 eV, frequency f = E/h = 4.59 x 10^14 Hz, and wavelength λ = c/f = 6.53 x 10^-7 m = 653 nm. If we have a few bazillion of these photons (give or take), we have a classical electromagnetic wave with that frequency and wavelength. How much is a bazillion? Consider sunlight at the Earth's surface. Hold up a 1 m^2 screen facing directly towards the sun on a clear day, and in one second it will receive about 1500 joules of electromagnetic energy. The light contains all visible wavelengths, of course, but let's pretend it's monochromatic with wavelength 653 nm. Then each photon carries 1.9 eV = 3.04 x 10^-19 J of energy, so one second's worth of light on the screen contains about 1500 / (3.04 x 10^-19) = 4.93 x 10^21 photons.
 Ok, so a classical electrometric wave is just lots of photons. The frequency of the photons is the same as the classical wave which they make. Now here's the clincher that I've been trying to get straight here for some time. Isn't the wave in a photon essentially a probability wave, or a De Broglie wave? So, does not the everyday characteristics of classical electromagnetic waves: color, focus ability, diffraction, etc. all come from photons’ probability waves?
 Mentor Basically, yes, but the connection is not simple. A large collection of photons with given frequency corresponds to a classical electromagnetic wave with that frequency, but don't fall into the trap of thinking of a photon as a tiny little bundle of classical electric and magnetic fields. The "photon field" is actually the quantized version of the classical electric potential and magnetic vector potential, which in relativity theory combine to form the "four-potential" Aμ. In quantum field theory, Aμ gets turned into an operator and quantized.

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 Isn't the wave in a photon essentially a probability wave, or a De Broglie wave?
I'd say the "The wave 'in a photon' is a physical wave; the probability wave, or wave function, is a probability function consisting of both real and imaginary components..."
but I think these words would/could still be debated today....

I came across nice dynamic illustration and introductory explanation here:

http://en.wikipedia.org/wiki/Wave_function

from

http://arxiv.org/PS_cache/hep-th/pdf/9702/9702027v1.pdf

my adds inside {}....

 In 1926, in one of the very first papers on quantum mechanics, Born, Heisenberg and Jordan presented the quantum theory of the electromagnetic field....... Born et al. gave a formula for the electromagnetic field as a Fourier transform {classical, continuous} and used the canonical commutation relations to identify the coefficients in this Fourier transform as operators that destroy and create photons, {annihilation and creation operators} so that when quantized this field theory became a theory of photons. Photons, of course, had been around (though not under that name) since Einstein’s work.... but this paper showed that photons are an inevitable consequence of quantum mechanics as applied to electromagnetism.

Also, what we today call Planck's constant started out as the "quantum of action". As usual in science evolution, such discrete interactions were not grandly theorized all at once, and I don't know which led to which, but Planck apparently needed a 'h' factor via the development of
"Classical statistical mechanics which requires the existence of h (but does not define its value)." apparently he was not at all sure any of this was a wise move:

 To save his theory, Planck had to resort to using the then controversial theory of statistical mechanics,[6] which he described as "an act of despair … I was ready to sacrifice any of my previous convictions about physics."[7] One of his new boundary conditions was
 In 1923, Louis de Broglie generalized the Planck relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but any particle. This was confirmed by experiments soon afterwards.

http://en.wikipedia.org/wiki/Plancks_constant

All the while Einstein's 1905 paper on the Photoelectric effect provided further theoretical support:

 In 1905, Albert Einstein ...... by describing light as composed of discrete quanta, now called photons, rather than continuous waves. Based upon Max Planck's theory of black-body radiation, Einstein theorized that the energy in each quantum of light was equal to the frequency multiplied by a constant, later called Planck's constant. A photon above a threshold frequency has the required energy to eject a single electron, creating the observed effect. This discovery led to the quantum revolution in physics and earned Einstein the Nobel Prize in Physics in 1921.
Heisenberg also utilized the Planck constant in his uncertainty principle [1927] and this became more theoretically developed in the following years.

Exactly what some of the means is still debated/discussed in these forums...a LOT.

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Here is a different view I finally found in my notes:

psi here the the quantum wave function...of the Schrodinger wave equation....

 No one can understand this theory [Bohmian mechanics] until he is willing to think of psi as a real objective field… Even though it propagates not in 3-space but in 3N-space. There is nothing in this theory but the wavefunction. It is in the wave function that we must find an image of the physical world, and in particular of the arrangement of things in ordinary three-dimensional space. [John Bell, 1987]

http://www.physicsforums.com/showthr...=551554&page=2

 ABSTRACT: Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state represents. There are at least two opposing schools of thought, each almost as old as quantum theory itself. One is that a pure state is a physical property of system, much like position and momentum in classical mechanics. Another is that even a pure state has only a statistical significance, akin to a probability distribution in statistical mechanics.