The case E0, the particle is unconfined and corresponds to a scattering problem. It is possible for the particle to be bound, or unbound. For the finite well, two cases must be distinguished, corresponding to positive or negative values of the energy E. By doing so, the potential is symmetric about x=0, giving rise to parity (Note: this could also be applied to a symmetric infinite wells). In this example, the origin of the x-axis was chosen at the center of the well. We have the following potential, V(x), given by the boundary conditions shown in Figure 2.1: We consider a potential well of height V0.įigure 2.1 Square well with finite potential. The particle is again confined to a box, but one which has finite, not infinite, potential walls. This type of problem is more realistic, but more difficult to solve due to the yielding of transcendental equations. The main difference between these two systems is that now the particle has a non-zero probability of finding itself outside the well, although its kinetic energy is less than that required, according to classical mechanics, for scaling the potential barrier. The finite potential well is an extension of the infinite potential well from the previous section.
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