In this section we will try to produce the potential energy function of a particle within a rigid box. Even though we know that there exists no real box which has perfectly rigid walls we will make this assumption. We establish a coordinate system within the box having boundaries at x=0 and x=L, yet we must produce the necessary insight (text).
1. The particle can move freely between 0 and L at constant speed and thus with constant kinetic energy.
2. No matter how much kinetic energy the particle has, its turning points are at x=0 and x=L.
3. The region x<0 and x>L are forbidden. The particle cannot leave the box.
So the potential energy function in this case would be
1. The particle can move freely between 0 and L at constant speed and thus with constant kinetic energy.
2. No matter how much kinetic energy the particle has, its turning points are at x=0 and x=L.
3. The region x<0 and x>L are forbidden. The particle cannot leave the box.
So the potential energy function in this case would be
Note: the particle only has kinetic energy.