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math-ph2012★ 7 cited
The fractional Schrödinger equation and the infinite potential well - numerical results using the Riesz derivative
Richard Herrmann
Based on the Riesz definition of the fractional derivative the fractional Schrödinger equation with an infinite well potential is investigated. First it is shown analytically, that…
math-ph2007★ 65 cited
Gauge invariance in fractional field theories
Richard Herrmann
The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order in the coupling constant .…
math-ph2005★ 6 cited
Properties of a fractional derivative Schroedinger type wave equation and a new interpretation of the charmonium spectrum
Richard Herrmann
Based on the Caputo fractional derivative the classical, non relativistic Hamiltonian is quantized leading to a fractional Schroedinger type wave equation. The free particle soluti…