Alex;
I find myself in the same boat as you !
There are so many concepts, theorems, principles etc, involved in all this QM material, I also find it very difficult to comprehend. I'm not so worried when I watch YouTubes of Feynman lectures though, (like the one Steven posted the other day), where he is also pointing out what he stuggled with, as well.
Most of what they write invariably seems to be expressed in terms of analogies and concepts, which I guess are fine, provided one can even understand the analogies & concepts !
I guess this is because the theory is all coming from the physical expression of what's going on .. in the language of maths. (I don't think maths coaching will help much here, either by the way …
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This article goes into a better explanation of 'weak' measurements (such as the two slit experiment article I posted). It also helped me in visualising wavefunctions also. Here's a good quote from it:
Quote:
Lundeen likens tomography to mapping the shape of a ripple on the surface of a pond (the wavefunction) by taking snapshots of the shadows of the ripples on the bottom. By combining information from many snapshots, the shape of the ripple can be inferred. In quantum tomography, however, each snapshot measurement is so "strong" that it destroys the ripple and the process must be repeated with identical ripples. Beyond the destructive nature, certain wavefunctions such as atomic or molecular orbitals cannot be determined using tomography.
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"While tomography is a global measurement that is more a reconstruction of the wave function, our measurement is local and direct." he explained. "The simple benefit of our research is that we now have an operational textbook definition of a wavefunction...something that is essential."
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So from this, apparently to date, they haven't really ever had a good consensus definition of what a wavefunction is.
This would seem to be a crucial first step in bringing it all closer to a grounded physical, real-world level, eh ?
Cheers