When to use the particle in a box equation

[hollyf]

Hi, I am confused about how and when to use this equation. What keywords should I look for in a question to know when to use this equation? Thanks!

[Mikayla_Weinhouse_2F]

Hi! The particle in a box model describes a particle free to move in a small space surrounded by impenetrable barriers. I believe the model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In terms of keywords in problems, I don't think there is a particle in a box equation, rather the Schrödinger Equation is used to solve problems of this type.

[Lexi Brownsberger 2E]

This equation is used when dealing with a particle moving horizontally within an "infinitely deep well" that it cannot get out of. The particle can have possible values of E and ψ as solutions. E is the allowed energy values and ψ(x) is a wavefunction. When ψ(x) is squared, it gives the probability of determining the location at a certain position of the particle within the box at a specific energy level.