A study of Fermionic Cooper pairs

The present paper describes a quantum mechanical study of Cooper pairs from the point of view of Fermion pair correct spin. The basic idea of building the theory consists of describing each particle with an appropriate Gaussian function, transforming them into a soft quantum mechanical object. From here, a new orthonormalized basis set with adequate symmetry is constructed, and then one can easily build the two-particle spin functions and the two-particle energies. As the particle energies become repulsive, one can add a harmonic oscillator term to stabilize the initial Hamiltonian expectation values. Results indicate that a way to extend the description of Cooper pairs to N Fermion particles becomes a straightforward consequence of the theory developed here.

Automated summary

The present paper provides a quantum mechanical study of Cooper pairs by considering the correct spin of the Fermion pair. The theory is built upon describing each particle with an appropriate Gaussian function to transform them into quantum mechanical objects. By constructing a new orthonormalized basis set with suitable symmetry, the two-particle spin functions and energies can be easily determined. Additionally, a harmonic oscillator term can be added to stabilize the initial Hamiltonian expectation values when the particle energies become repulsive. The results demonstrate the straightforward extension of describing Cooper pairs to N Fermion particles based on the developed theory.