Finite vs. Infinite Square Well potential base question

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SUMMARY

The discussion clarifies the difference in potential energy settings between the infinite square well and the finite square well in quantum mechanics. In Griffiths' treatment, the infinite square well is defined with a zero potential within a confined region, while the finite square well has a base potential set at a negative value of -V_0, where V_0 is a positive real number. This distinction is made because the infinite square well has infinite potential outside its boundaries, making it impractical to set a zero reference point outside the well. Conversely, the finite square well allows for a finite potential at infinity, justifying the zero reference point.

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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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