Unraveling the Mystery of Multiple Scattering in Double Well Systems

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In summary, the conversation discusses the ease of finding the resulting amplitudes of a double well system through the use of equations and periodic boundary conditions. The speaker questions why this process is so simple despite the complexity of the infinite reflections involved. The conversation concludes with a reference to John von Neumann's famous anecdote about summing infinite series.
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For a double well consider an incident wave from the left.
The wave gets transmitted and reflected at first well. The transmitted wave then hits the second well where it also gets both reflected and transmitted. The reflected part then hits the first well where it reflects and hits the second well and this process continues ad infinum. What I found was that it was not very hard to find the resulting amplitudes traveling in various directions if we just write up a system of equations and solve it (I think you have all seen how one applies periodic boundary conditions to the Schrödinger equation etc.) But why is it fundamentally so easy? I can't really see why it should physically be so easy since I have just accounted for how complicated the infinite process of reflections is. What is the miracle here?
I guess it is a stupid question since I should just accept the maths..
 
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This is like the well-known anecdote about John von Neumann...

"What trick?" asked von Neumann; "all I did was sum the infinite series."
 
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Thank you :)))
 

FAQ: Unraveling the Mystery of Multiple Scattering in Double Well Systems

What is the concept of "Scattering from double well"?

"Scattering from double well" refers to the phenomenon of a wave or particle encountering a potential energy barrier with two distinct wells, resulting in the wave being split into two separate components that are then scattered in different directions.

What is the significance of studying scattering from double well?

The study of scattering from double well is important in many areas of physics and chemistry, as it can provide insight into the behavior of particles and waves in various systems. It can also be used to understand the properties of materials with double well structures, such as semiconductors or molecules.

How is scattering from double well mathematically described?

The mathematical description of scattering from double well involves solving the Schrödinger equation, which is a differential equation that describes the behavior of quantum particles. This equation takes into account the potential energy barrier and the wave function of the particle to determine the probability of scattering in different directions.

What factors affect the scattering from double well?

The scattering from double well is influenced by several factors, including the height and width of the potential energy barrier, the energy of the incident particle or wave, and the shape of the potential energy well. Additionally, the quantum nature of particles and waves must also be considered in the scattering process.

What are some real-world applications of scattering from double well?

Scattering from double well has many practical applications, such as in the design of electronic devices, the study of chemical reactions, and the development of new materials. It is also used in medical imaging techniques, such as MRI, to analyze the scattering of particles in the body.

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