# Ground state of a finite well

1. Dec 8, 2009

### RedX

If you make the length of a finite well shorter, then the energy levels should increase, because for example the uncertainty principle. But can the ground state, when squeezed, have such high energy that the energy is greater than the potential of the well? Does that even make sense?

2. Dec 8, 2009

### kof9595995

what do you mean by "energy is greater than the potential of the well"? Do you mean E=K+V>V? But that's always true. Or do you mean total energy is higher than the height of the well, e.g. E=K+V>|V|, in this case since E>0 it's not a bound state let alone ground state.
And I think the uncertainty principle is not a very good way to analyze finite square well, because the particle is not strictly confined inside the well, you can't know for sure the narrower the well is, the smaller delta x is (I don't know if this is true in finite square well case, but anyway you shouldn't simply conclude that without calculation). But I think probably it's ok (but still not rigourously correct) to use it analyze infinite square well,because the particle is not allowed to go outside.

3. Dec 8, 2009

### RedX

I should have been more careful and instead of saying "energy is greater than the potential of the well", I should have said, like you mentioned, "greater than the height of the well."

4. Dec 8, 2009

### statespace101

Yes, it's called quantum tunneling.

5. Dec 8, 2009

### kof9595995

No, if the energy is already higher than a barrier,it's not called a tunneling.

6. Dec 8, 2009

### kof9595995

Anyway, I don't think OP's concern will come true, ground state in finite square well indicates a negative E (conventionally take the potential to be 0 outside the well), and a finite square well always at least possesses one bound state, e.g. the ground state, no matter how shallow or narrow the well is.

7. Dec 8, 2009

### statespace101

If the energy is negative wouldn't that mean there's still a non-vanishing probability that the well will fluctuate around the ground state? Then again it would be impossible to even get a probability right?

8. Dec 9, 2009

### kof9595995

Why would the well fluctuate? Finite square well is a potential well with definite height