Infinite-Finite Potential Well

[AKG]

I need help with this question. I'm not sure exactly what it wants (what does it mean by bound state) and how should I start the problem? Here it is:

Consider a particle of mass m moving in the following potential:

• $\infty$ for $x \leq 0$
• $-V_0$ for $0 < x \leq a \ (V_0 > 0)$
• $0$ for $x > a$

Calculate the minimum value for $V_0$ (in terms of a, m, and the Planck constant) so that the particle will have one bound state.

I guess what they're asking for is the smallest value for $V_0$ such that some particle will have energy E such that $-V_0 < E < 0$. So, if I can find the energy of the particle that is negative but closest to zero, that value will be $-V_0$. Is this right so far? If so, how do I go about finding E?

 

[Galileo]

The way I would go about this problem is by solving the Schrödinger equation and finding the energies. Assuming $-V_0<E<0$.

Then find the value of $V_0$ for which there is only one state with an energy<0.

I solved the finite potential well in the past, but don't remember it well enough to know if this is doable.