Relativistic Energy Spectrum of a Completely Confined Particleand Fowler’s Treatment on Electron Assemblies with Relativistic Energies

We give an analytical expression for the relativistic energy spectrum of a particle completely confined in a one-dimensional limited length in real space, based upon the wave property of particles, the relativistic energy-momentum relation and two mathematical formulas. Fowler’s treatment using a relativistic energy momentum relation of progressive waves in the electron assemblies in an enclosure, is justified in the large volume limit, by using the analytical expression obtained.