[¯|¯] Cold Fusion and Quantum Entanglement

Aprile 15th, 2026 | by Marcello Colozzo |

fusione fredda, entanglement quantistico,equazione di schrödinger — .

As seen in post precedente,the system must be in a state of total orbital angular momentum

with eigenvalue l=0, so that the potential barrier can be "thinned." Therefore, the most general orbital wave function can be written:

where u_E(r) are the eigenfunctions of the energy (recall that the spectrum of the Hamiltonian of this system is purely continuous), c(E) are the coefficients of the expansion of ψ in terms of eigenfunctions, so

where we have in the integrand a dependence only on r and not on the angular variables θ,φ, since for l=0 it is m_l=0 and therefore

Rammentiamo poi che R(r) is expressed as

where y(r) is a time-independent solution of the differential equation (Schrödinger equation) for a particle of mass µ moving in the potential V(r)=e²/r^ß):

Taking into account the spin degrees of freedom, we have that the overall wave function is written:

where the spin part is written in the total spin momentum representation:

Recall that the orbital part ψ(r) is written in the system of the center of mass and the relative coordinate. To be able to apply the symmetrization postulate (we have a system of two fermions), we must rewrite this wave function in the usual reference system. Specifically, if x₁ and x₂ are the position vectors of a single proton, we have:

By the symmetrization postulate, the wave function must be antisymmetric with respect to particle exchange. The orbital part is symmetric, so for the product to be antisymmetric, the total spin state must have a singlet state, which, as is known, is antisymmetric. Therefore, we have the quantum numbers:

Moving to the representation of the spin angular momentum of a single proton, with the obvious meaning of the terms, we have:

that is, a Bell state which, as is known, plays a fundamental role in Quantum Entanglement processes. However, here we have an opposite situation. For example, in a typical low-energy proton-proton scattering process, two protons interact via the Coulomb potential; they are first brought together to form a composite system. The Pauli exclusion principle (essentially, the antisymmetry of the wave function) forces the system into a state with quantum numbers l = 0 and s = 0 (spin singlet), hence a Bell state as far as the spin variables are concerned. Due to the repulsive potential and the low energy initially supplied to the protons to bring them together, the particles scatter and are simultaneously entangled.

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