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Guaicai
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How the symmetric and antisymmetric have results: A=0,G=H and B=0,G=-H in last picture ?[emoji53]
Some questions about the Finite Potential Well
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In summary, a finite potential well is a concept in quantum mechanics that describes a potential barrier with finite height and width. It creates a bound state for particles, leading to quantized energy levels and the phenomenon of tunneling. Compared to an infinite potential well, it allows for the possibility of particles passing through the barrier and has a continuous spectrum of energy levels. The depth and width of a finite potential well affect the energy levels and probability of finding particles within it. This concept has various real-world applications in fields such as quantum computing, nuclear physics, solid-state physics, and the study of chemical reactions and electron behavior. It also helps in understanding the energy states of atoms and molecules, with implications in chemistry and biology.
How the symmetric and antisymmetric have results: A=0,G=H and B=0,G=-H in last picture ?[emoji53]
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blue_leaf77
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Take a pencil and a paper then try drawing the symmetric one first where you have to substitute A=0, G=H into ##\psi_1##, ##\psi_2##, and ##\psi_3##. How does the resulting curve looks like if you make the ##x=0## line as a symmetrical line? Do the same for antisymmetric solution.Guaicai said:How the symmetric and antisymmetric have results: A=0,G=H and B=0,G=-H in last picture ?
Related to Some questions about the Finite Potential Well
1. What is a finite potential well?
A finite potential well is a concept in quantum mechanics that describes a potential barrier with finite height and width. It is often used as a model to understand the behavior of particles in confined spaces, such as atoms or nuclei.
2. How does a finite potential well affect the behavior of particles?
A finite potential well creates a bound state for particles, meaning that they are confined to a specific region within the well. This leads to quantized energy levels for the particles, as well as the phenomenon of tunneling, where particles can pass through the barrier even though they do not have enough energy to overcome it.
3. What is the difference between a finite potential well and an infinite potential well?
An infinite potential well has barriers that are infinitely high, meaning that particles cannot pass through them. In contrast, a finite potential well allows for the possibility of particles tunneling through the barriers. Additionally, an infinite potential well has a discrete set of energy levels, while a finite potential well has a continuous spectrum of energy levels.
4. How is the behavior of particles affected by the depth and width of a finite potential well?
The depth and width of a finite potential well determine the energy levels and probability of finding particles within the well. A deeper well will have higher energy levels and a larger probability of finding particles inside, while a wider well will have lower energy levels and a smaller probability of finding particles inside.
5. What real-world applications does the concept of a finite potential well have?
The concept of a finite potential well has applications in various fields, such as quantum computing, nuclear physics, and solid-state physics. It is also used in the study of chemical reactions and the behavior of electrons in semiconductor devices. Additionally, it helps in understanding the energy states of atoms and molecules, which has implications in fields such as chemistry and biology.
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