More on Phases: The Effect of Magnetic Fields

Abstract

The interactions of electric and magnetic things and the discovery that they are describable in terms of fields has been a source of wonder from the early 19th century to the present day. H.C. Oersted discovered that electric currents produce magnetic fields whose lines of force circle around them, and Michael Faraday discovered that changing magnetic fields produce changing currents of electrons, which in turn circulate around their lines of force. Finally, it was found that electrons in the presence of static magnetic fields circle in orbits about magnetic field lines. How does this affect the quantum theory of electrons? These electron orbits being oscillators, their energies must be quantized. This is the simplest of all quantum problems; the electron energies are simple multiples of a definite quantum energy. The classical orbits, or the quantum wave functions, turn out to have dimensions such that the magnetic field flux through a circle of such dimensions is an integral multiple of a simple “magnetic flux quantum” of magnitude hc\2e (h is Planck’s constant, c the speed of light, and e the electron charge). The phase of the wave function changes by 2π as one goes around the magnetic flux lines and changes continually with angle during the cycle.