In quantum physics, two highly important problems are the "particle in an infinite potential well" and the "simple harmonic oscillator." These are of such importance that solving them provides deep introduction with fundamental quantum concepts, including the wave function, energy quantization, applying boundary conditions, and even operational concepts. Each of these two problems, in a way, serves as a simplified model for understanding atomic and molecular structures. Many electronic and optical features of atoms and molecules can be interpreted using these two basic quantum examples. The development of new quantum concepts (such as collisional forces, quantum statistics, and others) can also be readily understood using these two simple quantum models. In the present paper, an anharmonic quantum oscillator is placed within an infinite-wall quantum well and its governing Schrodinger equation is solved using a finite difference algorithm in a home-made Mathematica code.
