Manaf,
Consider some electromagnetic radiation at a given frequency f .
From the classical point of view, the intensity of this radiation (I in W/m²) can be any positive number.
In quantum mechanics, a EM radiation is a flux of discrete lumps of energy, called photons. Therefore, you can define the photon flux N in photons/s/m². Quantum mechanics tells us also that the energy of these lumps is given by the Planck constant: E = h f . And therefore, the intensity of a radiation is now quantized: I = N h f, where N is the number of photons per second and meter² (photons/s/m²).
When the intensity of radiation is high, like the light in our rooms, the flux of photons (N) is so high that everything looks classical. But if you equip yourself with very sensitive detectors and if you decrease very much the intensity of light (radiation), then it is possible to see the photons individually.
Now concerning the BB 'continuous' spectrum. The spectrum is determined by the possible frequencies that could live in the box. This is related to the size of the box.
In classical physics, assuming the box is a conductor, the electric field must vanish on the wall of the box. The result is that the wavelengths of the radiations must be some integer fraction (i) of the size of the box (L). And therefore, the possible frequencies have a discrete spectrum: f = i c/L (c is the speed of light). This may look a bit more complicated if the full geometry is taken into account.
Consider now a box of 1 meter. Since c = 300 000 000 m/s, you get the following frequency spectrum in the box: f = i * 300 MHz. This means that the classical spectrum is a set of frequencies separated by 300 MHz. This may look like a big frequency gap. But you should compare this frequency gap with the observed frequency range. Looking in the visible spectrum, this is really a very small frequency gap: visible frequencies are between 440 THz and 750 THz. Therefore, the frequency gap plays no role in the visible spectrum (say temperatures above 1000°C), since this represents less than 1/100000000 from the width of the visible spectrum.
If you now consider lower temperatures, then the emission spectrum may shift to much lower frequencies, and then the classical discreteness of the frequency spectrum will be seen. And the size and even the shape of the box will play a big role.
In quantum physics, the spectrum of the BB radiation is exactly the same as in classical physics. By the word 'spectrum', I mean the set of possible frequencies. But the difference is in the intensities. The famous UV catastrophe disappears once the photon assumption and the Planck formula are taken into account. This means that in the ultraviolet part of the spectrum quantum physics explains the observed spectrum, while classical physics gave a divergence. This difference between QP and CP simply reflect the existence of photons.
And there is much more to say. As you know, the Planck formula has been soon applied by Einstein and others to electrons and particles. The energy levels of electrons in the atoms are explained again by the Planck formula. But now, the discreteness of the frequency set is a consequence of the Planck formula. Indeed, electrons also behave as waves (with a certain frequency and energy related by E=hf). And therefore, a "resonnance condition" arises, similar to what I explained for the BB, not all frequencies are possible. And a big difference with the BB is that, for atoms, the frequency gap plays a big role, it explains the emission spectra for example.
Michel
