A study of Fermionic Cooper pairs

• Published in: Journal of mathematical chemistry Vol. 61; no. 9; pp. 1916 - 1923
• Main Authors: Carbó-Dorca, Ramon, Nath, Debraj
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.10.2023; Springer Nature B.V
• Subjects: Chemistry; Chemistry and Materials Science; Cooper pairs; Electrons; Energy; Fermions; Hamiltonian functions; Harmonic oscillators; Integrals; Math. Applications in Chemistry; Original Paper; Particle spin; Physical Chemistry; Quantum mechanics; Theoretical and Computational Chemistry; Gaussian particle description; Two-particle wave functions; Fermion extension; Cooper pairs; Two-particle Hamiltonians; Two-particle stabilizing correction
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-023-01499-z

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.