System with Lowest Zero Point Energy in a 1D Box
The system with the lowest zero point energy when confined to a one-dimensional box of length is the particle in a box with a free particle. This system has the lowest possible energy due to the constraints of the box and the nature of the particle.

Particle in a Box
- In the particle in a box model, a particle is confined to a one-dimensional box of length L. The particle's energy is quantized due to the boundary conditions imposed by the box.
- The lowest energy level, known as the zero point energy, occurs when the particle is in its ground state with the lowest possible energy.

Free Particle
- A free particle is not confined to a box and can move freely in space. It has no potential energy in this case.
- The energy of a free particle is determined solely by its kinetic energy, given by the expression $\frac{p^2}{2m}$, where p is the momentum of the particle and m is its mass.

Lowest Zero Point Energy
- When a free particle is confined to a one-dimensional box, its energy is determined solely by its kinetic energy.
- In this scenario, the free particle will have the lowest possible energy, as it is not constrained by any potential energy terms and is free to move within the box without any additional restrictions.
Therefore, the system with the lowest zero point energy when confined to a one-dimensional box of length is the particle in a box with a free particle, where the energy is solely determined by the kinetic energy of the particle.