The 1-Dimensional Particle-in-a-Box

• A 1-D PIAB is closely related to the Free Particle, the difference being that there are walls of infinite potential energy that contain the particle.
• Inside the box, we assign the potential energy to be 0, while outside it is infinite.
• Because of this confinement, the energy states ARE quantized and only certain values are allowed.
• Since the particle is viewed as "bouncing" back and forth between the two sides, the trig solutions (cos) are preferred, being associated with a standing wave inside the box.
• The boundary conditions are what differentiate the PIAB solutions from the Free Particle solutions and new counter - the quantum number "n" - the identifies each solution (each wavefunction) and the associated energy.