Particle in a box

[sarahwu3a]

For a particle in a box, the textbook mentions that the particle has zero potential energy inside the box and infinite potential energy outside of the box. Why is this?

[Selena Yu 1H]

A particle in a box has zero potential energy inside the box because it has kinetic energy. Since, the particle is inside the box it's constantly moving around because it keep hitting the walls/sides of the box giving it kinetic energy and since it has kinetic energy it would have zero potential energy. However, once the particle is outside the box it has infinite potential energy because it is no longer moving around hitting the sides of the box which means that it is idle and according to the conservation of energy the kinetic energy can't just disappear, instead it was converted into potential energy. Hope this helps!