2.2.1: Particle in a Box

• The particle in the box is a model that can illustrate how a wave equation works.
• The particle in the box is a hypothetical situation with a particle trapped in a one-dimensional "box".
• The particle-wave can only exist inside the walls, along the x axis.
• The potential energy is zero because the particle is in an energetically-favorable position.
• Outside the box, the particle cannot exist and the potentially energy is infinitely large.
• It is infinitely unfavorable for the particle-wave to exist outside the box, so it never does.
• The particle in a box lets us consider a simple version of the Schrodinger equation.
• Energy is quantized because n is an integer, making n a quantum number.
• x = 0 is analogous to the nucleus in an atom.
• x = a is analogous to a boundary surface far from the nucleus.
• A change in sign of the wavefunction is a node.