To understand this, let's consider an example. Imagine a particle moving along the x-axis, and there is a potential energy function, \(V(x)\), that varies with position. If the particle's energy, E, is lower than the potential energy at any given position outside of a finite region (meaning \(E < V(x)\) for those positions), then the particle is not able to overcome the potential energy barrier and is trapped within the potential well.
On the flip side, if the energy of the particle, \(E\), is greater than the potential energy, \(V(x)\), at any position, it means that the particle has enough energy to overcome the potential energy barrier. In this case, the particle is not bound to the potential well and can move freely in that region.
In summary, if the energy of a particle is lower than the potential energy outside of a finite region, the particle is bound within that potential. It cannot escape and is confined to that particular area. Conversely, if the energy of the particle is higher than the potential energy, the particle is not bound and can move freely in that region.
Glosari:
"bound" refers to the particle being confined or trapped within a certain region of space due to the potential energy. On the other hand, "unbound" means the particle is not confined and can move freely.
If the energy of the particle, \(E\), is less than the potential energy, \(V(x)\), \(E<V(x)\) outside of a finite region of space, then the particle is bound within that potential.
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