Question

What are meant by bound and unbound states, and how can certain 1D potentials have both bound and unbound states?

Answer 1

A bound state describes a system where a particle is placed in a potential such that, the particle have tendency to ramain in a localized region. The potential may be either an external potential, or may be the result of the presence of another particle.

Answer 2

If , the particle isn’t bound at all and is free to travel from negative infinity to positive infinity. it is called unbound state.

Answer 3

Mm, I gathered that much from reading http://en.wikipedia.org/wiki/Bound_state . The latter half of my question is what I'm more perplexed by as it seems counter-intuitive at face value. Just to reiterate; how can certain 1D potentials have both bound and unbound states?

Answer 4

Take the example of a square well with a finite potential. When the energy of a particle in the box is less than that of the box's potential, the particle is confined to the box and is thus bound. If the particle's energy is greater than the potential, the particle is no longer bound.

Attached is an example showing several bound states for a particle in a square well.

Answer 5

Here's an image that shows an unbound state for a particle in square well. Note that both these images show a well with a limited potential, which is to say a finite depth. Also note that the images show actual wave functions.