LOL chart: Initial State: A child on a sled is in motion at the bottom of a small hill.
Final State: The child is in motion at the top of the small hill.
Notes: The system includes the child and the Earth. Resistance forces are
negligible. The child glides between initial and final state without any effort.

Aparticle of mass m is placed in a one-dimensional box of length l. the box is so small that the particle’s motion is relativistic, so that e p2/2m is not valid. (a) derive an expression for the energy levels of the particle using the relativistic energy–momentum relation and the quantization of momentum that derives from connement. (b) if the particle is an electron in a box of length l 1.00 1012 m, nd its lowest possible kinetic energy. by what percent is the nonrelativistic formula for the energy in error?