Purpose of Particle in a Box

[Meigan Wu 2E]

What is the purpose of the particle in a box concept, and what does it tell us exactly?

[Shash Khemka 1K]

The Particle in a Box problem, when solved, can give possible values of Energy and Wavefunction as well as the probability of pinpointing a particle's position inside the "box" at a specific energy level. To be honest, I am not 100% certain on how exactly to solve these kinds of problems myself but there are many resources online regarding the Particle in a Box problem.

Hope this helps!

[Emmaraf 1K]

Particle in a Box questions give us the right mindset to apply the Schrodinger's Equation since we can think of electrons as being the particles inside the box which is a molecule. We use the box concept to denote that that the particle can't be found outside the box (which is why the PE inside the box is 0) which is analogous to the idea that the electron can't be found outside the molecule (technically not 100% true due to tunneling but it works for the purposes of the application of Schrodinger's Equation). Then, since potential energy is equal to 0, the Hamiltonian operator of Schrodinger's equation only includes kinetic energy which simplifies the scenario.