Finite Square Well: Bond States and Asymmetric Potential Wells

[LagrangeEuler]

I am not sure how is it possible that asymetric potential well does not have bond states if $E<U_1<U_2$. In symmetric case solution always exists. Why this is a case?

 

[Nugatory]

I am not sure how is it possible that asymetric potential well does not have bond states if $E<U_1<U_2$. In symmetric case solution always exists. Why this is a case?

I may be misunderstanding the question here... The asymmetric finite square well does have bound state solutions.

 

[LagrangeEuler]

But not always. Right? Symmetric square well always has bound state solution.

 

[Misha]

For square (asymmetric) potential well an explicit equation with respect to energies of bound states is not difficult to derive. The existence of at least one bound state follows from that equation almost immediately.