The energy levels of the particle in a box are related to those of the free particle. For the free particle the wave vector, k, can have any value. For the particle in a box the wave vector has specific values determined by the boundary conditions, k = n pi/L. The energy increases as the square of the quantum number n. The spacing of the energy levels depends on the length L. As the box length increases the energy level spacing decreases. This feature is important for applications of the particle in a box model.