19: Analytically Soluble Models
The TISEq can be solved analytically only in a few special cases. In this section, we will analyze the main four. Luckily, we can use these solutions to explain most of the effects in chemistry since we can combine them to describe the hydrogen atom upon which we can build more complex chemical systems, as we will show in the next chapters.
Thumbnail: The quantum wavefunction of a particle in a 2D infinite potential well of dimensions \(L_x\) and \(L_y\). The wavenumbers are \(n_x=2\) and \(n_y=2\). (Public Domain; Inductiveload ).