Simple applications of Noether’s first theorem in quantum mechanics and electromagnetism

Abstract

Internal global symmetries exist for the free nonrelativistic Schrödinger particle, whose associated Noether charges, space integrals of the wavefunction and wavefunction multiplied by the spatial coordinate, are exhibited. Analogous symmetries in classical electromagnetism also are demonstrated. These results illustrate a number of subtleties associated with Noether’s first theorem.