when two sub atomic particals collide, being waves as well as particals. at point of collision do they act like radio waves and modulate each other. Are the resultant partical/waves produced by collision equivalent to upper and lower sidebands (as in AM modulation) or bessel functions (as in FM modulation) or both. or some other quantum equivalent? is E.M wave modulation a fair anology?
It's better to think of the collision as a closed room - some particles enter the room, something happens inside the room that we're not privy to, and when the interacting is done eventually some other particles emerge from the room. Quantum mechanics allows us to calculate probabilities for what comes out, but doesn't tell us much about what's going on during the interaction.
I think that could be one analogy too far. on a more familiar but similar track, I have an issue with the concept of the 'frequency' of a photon, even. A wave only has a single frequency is it extends from minus to plus infinity. This means that a photon must exist for all time and, if it doesn't, then it must have a finite extent. So how about the extents of different photons of the 'same' frequency, which have been produced or detected by different mechanisms? I am not after an answer to that question but it goes to demonstrate that mixing classical and quantum ideas together is fraught with danger.
There is a misconception here. The "wave" that is used to describe quantum behavior does NOT look and act like your typical EM wave. The EM wave is a physical wave. I can put an antenna somewhere, and actually measure the E and B field oscillation and display that on an oscilloscope. I can stick an electron in a cavity and it will wiggle that way I expected when it encounters such EM wave. The "wavefunction" in QM is a solution to the Hamiltonian/Schrodinger equation resulting in a "wave" that is NOT in real space, but rather in "configuration space"! You do not measure and detect such a wave in real space. You do not see anything oscillating. What you do detect is the combination of the probability density and the outcome of a measurement. You make many of these repeated measurement that may tell you of the validity of your original description of the system. You cannot simply use the idea that since the name given to it is a "wave", then it must have the same wave property as an ordinary EM wave. That would be incorrect. If you want to see how collision/scattering is dealt with in basic QM, you should start with the Born approximation: http://farside.ph.utexas.edu/teaching/qm/lectures/node69.html Zz.
But, Zapper, you cannot just dismiss any conclusion that are drawn from taking Wave Theory to a logical collusion just because de Broglie waves are non EM. Waves are just maths. Using de Broglie waves as a tool works, iirc, when the waves are standing waves (as in the solution to Schroedinger: Eigenvalues). Attribution of a 'wavelength' to a travelling particle is really a bit fanciful, imo, and so is the idea such waves being subject to classical processes.
But physics isn't just math. At some point, you do arrive at "unphysical" solution in many cases. I'll argue that the EM wave is a subset or a special case of all this, not just in terms of the math, but also in terms of the physics. If this were an argument made in some published journal, then I'd be more likely to pay more attention to it and see if there's something physical there. However, it is my impression that the common misconception of what the "wave" is in QM is at play here. Particle in physics do not act like "radio waves"! I've lost count how many times someone here asked how such particles oscillate like such waves, i.e. they thought these waves were the profile of the trajectories! But is this really what we are dealing with here with the OPs question and at that level of understanding? I seriously doubt it. Zz.
Well, yes; we could choose an appropriate 'level' to discuss this at but I still say the idea of modulation does not relate just to EM waves. It is a strictly mathematical issue and it seems quite reasonable to expect Modulation to be something that could be associated with any form of 'Wave'. Physics is, as you say, a subset of Maths and there are many possible Unphysics answers. Actually, 'a particle' never behaves like a wave. You need a lot of them for the two explanations (particle, wave) of a phenomenon to converge. I guess people use the "like Radio Waves" description as a shorthand for 'waves and all the associated theory'. Also, Modulation is usually analysed in terms of Frequency. You could, for instance, velocity modulate a beam of electrons and that would be modulating the de Broglie wavelength of the electrons. But there is no actual frequency (afaik) associated with these electrons, unless it's f=v/λ???. Likewise, if you were to alter the local fields inside an atom, (Zeeman and Stark effect??) you would be changing the 'wavelengths' of the electrons in it, which would be a form of modulation. But, again, what is the 'frequency' involved? Perhaps that's where the flaw lies - with 'mathematical', mechanical and EM waves, there is a basic c = fλ involved. Is there an equivalent for the the waves associated with matter?