Finite vs. Infinite Square Well potential base question

In summary, Griffiths places the base of the infinite square well at a zero potential and the base of the finite square well at a negative potential, which is a positive, real number. This is because for the finite square well, the potential goes to some finite value at x = ±∞, so it is convenient to set that value to zero. However, for the infinite square well, the potential is infinite outside of a small region, so setting it to zero within that small region is a convenient choice.
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Zacarias Nason
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I just noticed in reading Griffiths that he places the base of the infinite square well at a zero potential while he places the base of the finite square well at a negative potential -V_0, where V_0 is a positive, real number; is there any reason for this? I just started learning about them/am not too familiar with them so I may be missing the importance, but why aren't they both just placed at zero?
 
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It doesn't matter. But if your potential goes to some finite value at ##x = \pm \infty##, it's conventional and convenient to set that value to zero. That's what we do for the finite square well. For the infinite square well this is impossible, because the potential is infinite outside of a small region. So we may as well set the potential within that small region to zero, which is a convenient value.
 
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FAQ: Finite vs. Infinite Square Well potential base question

What is a finite square well potential?

A finite square well potential is a type of potential energy function commonly used in quantum mechanics to describe the behavior of a particle confined to a certain region. It is characterized by a finite depth and width, and is often used to model the behavior of a particle in a confined system, such as an atom or a nucleus.

What is an infinite square well potential?

An infinite square well potential is a type of potential energy function that is used to describe the behavior of a particle confined to a certain region with infinite potential barriers on either side. This means that the particle is completely trapped within the well and cannot escape. This type of potential is often used to model the behavior of a particle in a one-dimensional system, such as a quantum well or a quantum dot.

What is the difference between a finite and infinite square well potential?

The main difference between a finite and infinite square well potential is the depth and width of the potential well. In a finite square well, the depth and width are limited, allowing for the possibility of the particle to tunnel through the potential barriers. In an infinite square well, the potential barriers are infinitely high, making it impossible for the particle to tunnel through and escape from the well.

What are the applications of finite and infinite square well potentials?

Finite and infinite square well potentials have various applications in quantum mechanics, such as modeling the behavior of electrons in atoms, the behavior of photons in optical fibers, and the behavior of particles in semiconductor devices. They are also used in quantum computing, where the confined states of particles in these potentials can be used as qubits for information processing.

What are the limitations of using finite and infinite square well potentials?

One limitation of using finite and infinite square well potentials is that they are idealized models and do not accurately represent real-world systems. In reality, potential wells are not perfectly square and particles may interact with their surroundings, making the potential more complex. Additionally, these potentials only describe the behavior of particles in one dimension, which may not be sufficient for some systems. Therefore, it is important to consider the limitations of these models when applying them to real-world situations.

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