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 > aCalculate 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.