I have started learning QM and it says that we cannot deternine momentum and position or both of a particle acurately. There is an uncertainty in momentum ◇p and uncertainty in position ◇x . The uncertainty in position is explained by bragg's equation . But to describe uncertainty in momentum , they are saying that the particle is behaving like a wave and connect wavelength with momentum. If we assume matter to be particles can we measure momentum accurately? How do we measure momentum of an object?
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This may help. It is about photons, but the wave/particle duality applies to electrons - How can a red light photon be different from a blue light photon? – mmesser314 Dec 10 '23 at 15:01
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This may help - The more general uncertainty principle, regarding Fourier transforms. If you are comfortable with Fourier Transforms, it goes a long way toward making the uncertainty principle intuitive. And it explains Fourier Transforms. – mmesser314 Dec 10 '23 at 15:27
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Yes i will learn fourier transformation first – Dec 10 '23 at 15:34
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There are a few ways to think about the uncertainty principle.
The first is through fourier analysis. Position and momentum are fourier transforms of each other. Therefore, if we consider measuring position very accurately (a very narrow spike in the position representation), then the fourier transform of this spike will be a very wide wave in the momentum representation. Narrower in space = wider in momentum space and vice versa. Uncertainty therefore isn't due to experimental constraints, but is an intrinsic property.
Your idea of 'assuming' matter to be a particle also doesn't work. We can't do that. Electrons for instance have both particle like and wave like properties, you can't 'separate' the two.
Regarding how we actually measure momemtum, we're essentially just measuring speed. In particle accelerators, we do this by looking at how much a parricle's path curves in a strong magnetic field.
XBlake97
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Particle is confined to one point. And wave is present everewhere in space. So how can something be a wave and a particle at the same time. And how do we measure speed of particles apart from using particle accelerators like when it was not invented during hyesemberg 's times. – Dec 10 '23 at 14:58