Chronicles of Physics

ISSN: 2194-8704 (print)

ISSN: 2195-6472 (electronic)

Volume 1, Number 1, January 2013

Gam. Ori. Chron. Phys. 1(1), (2013)

Contents

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Richard Herrmann

The fractional Schrödinger equation and the infinite potential well – numerical results using the Riesz derivative

Richard Herrmann

abstract:

Based on the Riesz definition of the fractional derivative the fractional Schroedinger equation with an infinite well potential is investigated. First it is shown analytically, that the solutions of the free fractional Schroedinger equation are not eigenfunctions, but good approximations for large k and for $\alpha \approx 2$. The first lowest eigenfunctions are then calculated numerically and an approximate analytic formula for the level spectrum is derived.

Numerical solution of the fractional quantum mechanical harmonic oscillator based on the Riemann and Caputo derivative

Richard Herrmann

abstract:

Based on the Riemann- and Caputo definition of the fractional derivative we tabulate the lowest n=31 energy levels and generated graphs of the occupation probability of the fractional quantum mechanical harmonic oscillator with a precision of 32 digits for 0.50 < \alpha < 2.00, which corresponds to the transition from U(1) to SO(3).

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