Tunneling in Fractional Quantum Mechanics

Details Tunneling in Fractional Quantum Mechanics Tunneling in Fractional Quantum Mechanics

2010-11-09

arxiv.org/abs/1011.1948v2

Physics

Mathematical Physics

21 pages, 3 figures. Revised version; accepted for publication in Journal of Physics A: Mathematical and Theoretical

Scientific paper

We study the tunneling through delta and double delta potentials in fractional quantum mechanics. After solving the fractional Schr\"odinger equation for these potentials, we calculate the corresponding reflection and transmission coefficients. These coefficients have a very interesting behaviour. In particular, we can have zero energy tunneling when the order of the Riesz fractional derivative is different from 2. For both potentials, the zero energy limit of the transmission coefficient is given by $\mathcal{T}_0 = \cos^2{\pi/\alpha}$, where $\alpha$ is the order of the derivative ($1 < \alpha \leq 2$).

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