Undergrad Finite vs. Infinite Square Well potential base question

[Zacarias Nason]

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?

 

[The_Duck]

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.