2007/04/02 by Mushfiq Ahmad, Ahmad, Mushfiq
Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.0704.0153
4 pages
arxiv created 2007/04/02 · arxiv updated 2009/12/01
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.