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International Journal of Contemporary Mathematical Sciences

Fractional Schrodinger wave equation and fractional uncertainty principle

Muhammad I. Bhatti

Published Jan 1, 2007• 25 citations
Publisher
DOI
10.12988/ijcms.2007.07096

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This note shows that Heisenberg's choice for a wave function in his original paper on the uncertainty principle is simply a renormalized characteristic function of a stable distribution with certain restrictions on the parameters. Relaxing Heisenberg's restrictions leads to a more general formulation of the uncertainty principle. This reformulation shows quantum uncertainty can exist at a macroscopic level. These modifications also give rise to a new form of Schrodinger's wave equation as the equation of a vibrating string. Although a heat equation version can also be given, the latter shows the traditional formulation of Schrodinger's equation involves a hidden Cauchy amplitude assumption.