Finite Square Well and its Applications
DOI:
https://doi.org/10.54097/hset.v61i.10269Keywords:
Quantum mechanics, Kronig-Penney model, laser, finite square wellAbstract
The relation between finite square well and laser is paramount in quantum mechanics. This paper focuses on establishing the relationship between finite square well and laser through the most fundamental theory of quantum mechanics. This paper first introduced the importance of finite square well and the Kronig-Penney model in the development of the theory of laser and Quantum mechanics briefly. Then, this paper gives a detailed derivation of energy level finite square well through the Schrodinger equation. In the application section, we first introduced Bloch’s Law, a vital theorem for the following subsection. It describes the form of wave function under periodic potential. Then, the energy level of the finite square well is put into the application of the Kronig-Penney model, which is an infinite repetition of the finite square well. This part focus on the derivation of the energy level of the Kronig-Penney model. It applies both the energy level of the finite square well and Bloch’s Law. In the end, we note that the energy level of the Kronig-Penny model exhibits a band gap. It is an important phenomenon for lasers.
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