AN UNUSUAL QUANTUM ENTANGLEMENT CONSISTENT WITH SCHRODINGER’S EQUATION

. In this paper, a quantum system is considered to be formed by two free particles in such a manner that for at least one of its states, an Ansatz Ψ specifically modeled to present mathematical properties that could be consistent with an unusual quantum entanglement is proposed. The Ansatz Ψ is defined by an expansion in terms of the eigenfunctions of an arbitrary observable, which is associated, separately, with the considered particles, with coefficients given by the values of functions C n , initially free and dependent on the quotient of the separation between the particles and their Compton wavelength. It is shown that Ψ satisfies the corresponding Schr¨odinger equation under the requirement that the C n be of the square integrable type. The function Ψ corresponds to an entanglement which, in the absence of both a measurement and the performance of entanglement degrading agents, collapses to zero when a condition is satisfied.