Infinite-Finite Potential Well

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  • #1
AKG
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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:
  • [itex]\infty[/itex] for [itex]x \leq 0[/itex]
  • [itex]-V_0[/itex] for [itex]0 < x \leq a \ (V_0 > 0)[/itex]
  • [itex]0[/itex] for [itex]x > a[/itex]
Calculate the minimum value for [itex]V_0[/itex] (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 [itex]V_0[/itex] such that some particle will have energy E such that [itex]-V_0 < E < 0[/itex]. So, if I can find the energy of the particle that is negative but closest to zero, that value will be [itex]-V_0[/itex]. Is this right so far? If so, how do I go about finding E?
 

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  • #2
Galileo
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The way I would go about this problem is by solving the Schrödinger equation and finding the energies. Assuming [itex]-V_0<E<0[/itex].

Then find the value of [itex]V_0[/itex] 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.
 

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