Relationship to Schrodinger's Equation
Posted: Sun May 06, 2018 10:38 am
How does a particle in a box model Schrodinger's equation? In another post, it said that this model explains energy quantization since the box has infinitely high walls. Wouldn't there need to be a discrete amount of energy needed to pass the walls? Or does this model explain quantization in that the particle is trapped, so can only have one value in terms of energy?
Re: Relationship to Schrodinger's Equation
Posted: Sun May 06, 2018 2:36 pm
You are not expected to know about particle-in-a-box for the midterm. It is another system that can be modeled using the Schroedinger equation.
The particle is being modeled as a wave, just like we modeled the electron as a wave. These equations are modeling a particle in a box as a representation of an electron in an atom. In a sense, the size of the box is the size of an atom.
The particle may only occupy certain positive energy levels. It can never have zero energy, meaning that the particle can never "sit still". It is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at spatial nodes.