A square well potential is a simplified model used in quantum mechanics to describe the behavior of a particle in a confined region. It consists of a potential energy function that is constant inside a certain region (the well) and infinite outside of it.
A square well wave function is the mathematical representation of the behavior of a particle in a square well potential. It describes the probability of finding the particle at a certain position within the well and how it evolves over time.
A square well wave function is continuous and smooth at all points within the well, and goes to zero at the boundaries of the well. It must also be normalized, meaning that the total probability of finding the particle within the well is equal to 1.
The energy eigenstates in a square well potential are the allowed energy levels that a particle can have within the well. These states determine the behavior and properties of the particle, such as its momentum and probability of being found at a certain position.
The depth and width of a square well potential affect the energy eigenstates and the allowed energies of a particle within the well. A deeper well will have more energy levels and a wider well will result in lower energy levels. This ultimately affects the probability of finding the particle at certain positions within the well.