Bosons and Fermions: Indistinguishable Particles with Intrinsic Spin

If we imagine a Hamiltonian, H^(r1,r2), describing two identical particles at positions r1 and r2 and then we interchange the particles, the Hamiltonian will be unaffected, i.e. H^(r1,r2)=H^(r2,r1). If we introduce an exchange operator P^r1,r2 such that P^r1,r2H^(r1,r2)=H^(r2,r1)P^r1,r2=H^(r1,r2)P^r1,r2, we see that they commute, or [P^r1,r2,H^(r1,r2)]=0. We know then that P^r1,r2andH^(r1,r2) have common eigenfunctions. We can then easily show that the eigenfunctions of the exchange operator must be either even or odd. Experiments show that odd exchange symmetry corresponds to half-integer spin particles called fermions, while even exchange symmetry corresponds to integer spin particles called bosons. The notes then discuss the implications of the new postulate and then presents the Heitler–London theory and the Heisenberg exchange Hamiltonian which has been so successful in predicting molecular structure.

GENERATION OF VORTICES IN SUPERCONDUCTING DISKS

We study the nucleation of vortices in a thin mesoscopic superconducting disk and stable configurations of vortices as a function of the disk size, the applied magnetic field H and finite temperature T. We also investigate the stability of different vortex states inside the disk. Further, we compare the predictions from Ginzburg-Landau (GL) theory and London theory - the GL equations take the superconducting density into account, but the London equations do not. Our simulations from both theories show similar vortex states. As more vortices are generated, more superconducting regions will be destoryed. The GL Equations consider this effect and provide a more accurate estimate.

ELECTROSTATIC FIELD IN SUPERCONDUCTORS II: BALANCE OF FORCES

The London theory of diamagnetic currents is discussed from the magnetohydrodynamical point of view. It is argued that the motion of superconducting electrons is controlled by the electrostatic field which balances the Lorentz and the inertial forces.