A fractional Wheeler-DeWitt equation yields D-dimensional Schwarzschild-Tangherlini black holes, with the horizon called fractal and the temperature set by an arbitrary parameter alpha.
Fractional Schrodinger equation
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abstract
Properties of the fractional Schrodinger equation have been studied. We have proven the hermiticity of fractional Hamilton operator and established the parity conservation law for the fractional quantum mechanics. As physical applications of the fractional Schrodinger equation we have found the energy spectrum for a hydrogen-like atom - fractional ''Bohr atom'' and the energy spectrum of fractional oscillator in the semiclassical approximation. A new equation for the fractional probability current density has been developed and discussed. We also discuss the relationships between the fractional and the standard Schrodinger equations.
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Fractional Schwarzschild-Tangherlini black hole with a fractal event horizon
A fractional Wheeler-DeWitt equation yields D-dimensional Schwarzschild-Tangherlini black holes, with the horizon called fractal and the temperature set by an arbitrary parameter alpha.