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Register a new userReciprocal Symmetry and Classical Discrete Oscillator Incorporating Half-Integral Energy Levels
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Mushfiq Ahmad
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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.
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