Properties of the fractional derivative Schroedinger type wave equation and a new interpretation of the charmonium spectrum
نویسنده
چکیده
The definition of the standard derivative operator is extended from integer steps to arbitrary stepsize. The classical, nonrelativistic Hamiltonian is quantized, using these new fractional operators. The resulting Schroedinger type equation generates free particle solutions, which are confined in space. The angular momentum eigenvalues are calculated algebraically. It is shown, that the charmonium spectrum may be classified by the derived angular momentum eigenvalues for stepsize=2/3. The best agreement with experimental data is achieved with stepsize=2/π, which suggests an underlying SU(π) symmetry. PACS numbers: 12.39, 12.40, 14.65, 13.66, 11.10, 11.30, 03.65 Submitted to: J. Phys. A: Math. Gen.
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