A physical example approximating the idealized situation

In summary: This makes it impossible to accurately determine the position of the proton near the nucleus, as the uncertainty in its position is much larger than the size of the nucleus. In summary, the wave function of a proton in a cyclotron beam can be used to describe its position near a nucleus, but only if the beam is much longer than the dimensions of the nucleus.
  • #1
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From Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, Eisberg-Resnick:
"A physical example approximating the idealized situation represented by these
wave functions would be a proton moving in a highly monoenergetic beam emerging
from a cyclotron. Such beams are used to study the scattering of protons by targets
of nuclei inserted in the beam. From the point of view of the target nucleus, and in
terms of distances of the order of its nuclear radius r', the x position of a proton in
the beam may be for all practical purposes completely unknown. That is Δx » r'.
...In other words, near a nucleus the wave function of (6-9)
##ψ = Ae^{i(kx - wt)}##
can be used to describe a proton in a cyclotron beam directed towards increasing x,
providing the beam is extremely long compared to the dimensions of the nucleus—a
condition which is always satisfied in practice since nuclei are extremely small."
I don't understand why "the x position of a proton in the beam may be for all practical purposes completely unknown".
Thanks!
 
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  • #2
Typical beams have a width of micrometers to millimeters, while the target nucleus has a size of femtometers. Even if you look at a single proton in the beam, its wavefunction will be spread out extremely wide compared to the size of a nucleus.
 

FAQ: A physical example approximating the idealized situation

What is a physical example approximating the idealized situation?

A physical example approximating the idealized situation is a real-life scenario or experiment that closely resembles an idealized situation in order to better understand and test theoretical concepts.

Why is it important to have physical examples that approximate idealized situations?

Having physical examples that approximate idealized situations allows scientists to test and validate theoretical concepts in a controlled and practical manner. It also helps to bridge the gap between theory and real-world applications.

What are some common examples of idealized situations?

Some common examples of idealized situations include perfectly frictionless surfaces, perfectly elastic collisions, and ideal gases with no intermolecular forces.

How do scientists create physical examples that approximate idealized situations?

Scientists may use various tools and techniques, such as advanced equipment, mathematical models, and carefully controlled experiments, to create physical examples that closely resemble idealized situations.

What are the limitations of physical examples that approximate idealized situations?

While physical examples can provide valuable insights and understanding, they may not always perfectly replicate an idealized situation due to various factors such as external influences, limitations of technology, and inherent complexities of the natural world.

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