Behavior of charged particle motion along a magnetic field and a retarding potential-evidence for the existence of discrete energy states in classical mechanical domain

Abstract

We report here experimental results which point to a rather unexpected, astonishing behavior of charged particle motion in a magnetic field in the presence of a retarding electric potential. An electron beam, when energy scanned with respect to its 'parallel' energy using a retarding potential, the response of the transmitted current as a function of the retarding potential is found to be oscillatory as against the monotonic response, expected according to the standard initial value paradigm of classical mechanics. The unexpected 'peaks' and 'dips' in the transmitted current plots are interpreted as "allowed" and "forbidden" energy states of the system. The peaks (or dips) are found to fit very well with a theoretical relationship which motivated the search for such a behavior; also "quantum numbers" for the peaks have been identified. A very astonishing aspect of the relationship is the dependence of the energies of the allowed states on the length of the box.