How are properties connected to particles?
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Both Wave and Particle?
We have seen that the essential idea of quantum theory is that matter, fundamentally, exists in a state that is, roughly speaking, a combination of wave and particle-like properties. To enter into the foundational problems of quantum theory, we will need to look more closely at the "roughly speaking." It is needed since it is not so easy to see how matter can have both wave and particle properties at once. One of the essential properties of waves is that they can be added: take two waves, add them together and we have a new wave. That is a commonplace for waves. But it makes no sense for particles, classically conceived. Just how do we "add up" two particles?
Superpositions of Matter Waves
two slitsA distinctive characteristic of waves is that we can take two waves and add them up to form a new wave. That adding of waves is the essence of the phenomenon of the interference of waves. The theory of matter waves tells us that particles like electrons are also waves. So we should be able to add several of them together, just as we could add several light waves together.
Wave Packets
This example of superposition will help us resolve a little puzzle in matter wave theory. If particles are really waves, how can localized particles enter into the theory at all?
Recall de Broglie's relation.
momentum = h / wavelength
Heisenberg's "Uncertainty" Principle
The trade-off we have just seen between definiteness of position and definiteness of momentum is quantified by what is commonly known as Heisenberg's uncertainty principle. For reasons that I will explain shortly, I prefer to call it an "indeterminacy principle." It depends on using a standard statistical measure, the standard deviation, for the uncertainty or indeterminacy or, more colloquially, the spread in a wave packet.
if u more know
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/quantum_theory_waves/index.html&ved=2ahUKEwixls3SvLjdAhUcSY8KHeBSAGYQFjAKegQIBhAB&usg=AOvVaw1hq1oep-Udx4J4g9MN7ghi&cshid=1536858817437
We have seen that the essential idea of quantum theory is that matter, fundamentally, exists in a state that is, roughly speaking, a combination of wave and particle-like properties. To enter into the foundational problems of quantum theory, we will need to look more closely at the "roughly speaking." It is needed since it is not so easy to see how matter can have both wave and particle properties at once. One of the essential properties of waves is that they can be added: take two waves, add them together and we have a new wave. That is a commonplace for waves. But it makes no sense for particles, classically conceived. Just how do we "add up" two particles?
Superpositions of Matter Waves
two slitsA distinctive characteristic of waves is that we can take two waves and add them up to form a new wave. That adding of waves is the essence of the phenomenon of the interference of waves. The theory of matter waves tells us that particles like electrons are also waves. So we should be able to add several of them together, just as we could add several light waves together.
Wave Packets
This example of superposition will help us resolve a little puzzle in matter wave theory. If particles are really waves, how can localized particles enter into the theory at all?
Recall de Broglie's relation.
momentum = h / wavelength
Heisenberg's "Uncertainty" Principle
The trade-off we have just seen between definiteness of position and definiteness of momentum is quantified by what is commonly known as Heisenberg's uncertainty principle. For reasons that I will explain shortly, I prefer to call it an "indeterminacy principle." It depends on using a standard statistical measure, the standard deviation, for the uncertainty or indeterminacy or, more colloquially, the spread in a wave packet.
if u more know
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/quantum_theory_waves/index.html&ved=2ahUKEwixls3SvLjdAhUcSY8KHeBSAGYQFjAKegQIBhAB&usg=AOvVaw1hq1oep-Udx4J4g9MN7ghi&cshid=1536858817437
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₳nswer :
➨ We can take the example of refraction in glass slab that refracts of the away.
➥ The light that comes and enters in the glass slab is refracted in the slab.
➭ Points to be remembered in refraction
➠Refraction is a apprison in our eyes that seems to be happen but not really.
➠Refraction takes place in many types substances.
➠I have explained the the method of refraction in glass slab.
➠I refraction the checking should be properly done.
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