Dependence of Quantum Decoherence on Wavelengths of a Particle in One Dimensional Box

In this paper, de Broglies wave particle duality relation is applied to a particle in one dimensional box problem to find the constraint for quantum decoherence of this system. It is observed that, for a particle of mass m captured in one dimensional box of length L should follow the relation mL ≤ h/4c to have a stable quantum state where h is Planck’s constant and c is the speed of light in the vacuum space. Violation of this condition would lead to quantum decoherence of this system. It is also observed that if decoherence occurs, rate of decoherence would be inversely proportional to the square of the particle’s initial wavelength.