Reciprocal Symmetry and Classical Discrete Oscillator Incorporating Half-Integral Energy Levels
Abstract
Description
Classical oscillator differential equation is replaced by the corresponding (finite time) difference equation. The equation is, then, symmetrized so that it remains invariant under the change d going to -d, where d is the smallest span of time. This symmetric equation has solutions, which come in reciprocally related pairs. One member of a pair agrees with the classical solution and the other is an oscillating solution and does not converge to a limit as d goes to 0. This solution contributes to oscillator energy a term which is a multiple of half-integers.
4 pages
4 pages