## Help explaining a quantum wave function. (How you describe a wave by a particle)

 Quote by HomogenousCow These are probability amplitude densities (impressive word eh?), so basically you just take the modulus square of the function and then integrate over a section of space, and ta-da you have the probability of finding the particle (or whichever one you are looking for, different particles in the system have their own position basi) in that section of space.
By using the word 'finding' you are suggesting its there and you are determining where it is - such is not the case in all interpretations. I think you probably didn't really mean to imply that - just pointing out sometimes the language we use in this area can have subtleties to it.

Thanks
Bill

 Quote by nukeman I understand a normal mechanical wave, simply a disturbance that moves. But, I want understand a quantum wave function, mainly how you can describe a wave by the particle it self?
You can't. There are limits regarding what can be described using a particle formulation and what can be described using a wave formulation. Generally, the wave formulation describes pre-detection situations, and the particle formulation describes post-detection situations. The complementary relationship between the two is the basis of what's called the wave-particle duality in the orthodox or Copenhagen interpretation of the quantum theory. You might start with Heisenberg's "The Physical Principles of the Quantum Theory", and work forward from there.

Apparently, the nature underlying instrumental results has both wavelike and particlelike properties. The foundation of the old quantum theory is based on conceptualizations or inferences regarding visualizations of deep reality in terms of familiar notions of particles and waves in particulate media. However, modern quantum theory has become somewhat removed from these conceptualizations and the mathematical treatments of various instrumental phenomena have become abstract to the extent that they are less amenable to prior inferential conceptualizations.

So, how should one think about the Schrodinger equation, wavefunctions, etc.? Well, the only thing that's known for sure is that, so far, it's an effective way of modelling experimental preparations in terms of what might be called a probability mechanics. Any wavefunction, in qm, is a distribution of particulate amplitudes, the square of which is a predictor of probable instrumental (ie., particulate) results. Beyond that, regarding how it might relate to what's actually happening in the deep reality, is a matter of contentious speculation.

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 Quote by nukeman Can anyone answer this? If I have a molecule, or anything really (something very small)If it vibrates.... Are the quantum mechanical objects the molecule it self and the vibration and wave it gives off?
DeBroglie suggested this idea. He proposed that inside the particle there was a periodic process that was equivalent to an "internal clock". Thus, there was a physically ”real” particle that induces a physically relevant ”realistic” wave, and that wave in turn is capable of affecting further motion of the particle. This particle-wave association picture has been artificially induced (e.g. via external vibration frequency) on the macroscale by Couder's group:

Single-Particle Diffraction and Interference at a Macroscopic Scale
https://hekla.ipgp.fr/IMG/pdf/Couder-Fort_PRL_2006.pdf

Interestingly, there was a fairly recent paper suggesting some evidence for an internal clock:

A Search for the de Broglie Particle Internal Clock by Means of Electron Channeling