Quantum-state representations in a strong quantizing magnetic field: Pairing theory of superconductivity

Two of the commonly used basis states of an electron in a strong quantizing magnetic field (‘‘orbit center’’ and ‘‘angular momentum’’), their interrelation, and physical interpretations are described briefly here. Their relative utility in elucidating various physical aspects is exhibited by examining (1) the exact solution of the linearized superconducting gap equation, and (2) the matrix elements of a plane wave in both representations. It is shown that the two-particle matrix element of the contact interaction, V¯δ(${\mathbf{r}}_1$-${\mathbf{r}}_2$), in the orbit-center representation is separable in the relative orbit centers. A complete set of solutions of the linearized gap equation is thereby obtained.