Finite well penetration depths dependence on Well Length

[PsychonautQQ]

So in the infinite well Energy is proportional to 1/L^2, so I'm assuming in the finite well there is some sort of similar relation. So as the L decreases, the energy increases, so the wavelength decreases. Decreasing the wavelength means more energy, so it should penetrate further, but also if you draw the situation a smaller wavelength will make it penetrate less far, although the well also is getting smaller so blahh I'm trying to figure out how all this adds up. Thanks!

 

[The_Duck]

but also if you draw the situation a smaller wavelength will make it penetrate less far

What do you mean by this? I don't think it's correct.

I suggest you actually work through the solution of the finite square well and see how the penetration length of the ground state wave function depends on L.