In the present work, and along the lines of Hermann, ScR theory is applied to a finite one-dimensional square well potential problem. The aim is to show that scale relativity theory can reproduce quantum mechanical results without employing the Schrödinger equation. Some mathematical difficulties that arise when obtaining the solution to this problem were overcome by utilizing a novel mathematical connection between ScR theory and the well-known Riccati equation. Computer programs were written using the standard MATLAB 7 code to numerically simulate the behavior of the quantum particle in the above potential utilizing the solutions of the fractal equations of motion obtained from ScR theory. Several attempts were made to fix some of the parameters in the numerical simulations to obtain the best possible results in a practical computer CPU time within limited local computer facilities [1,2]. Comparison of the present results with the corresponding results obtained from conventional quantum mechanics by solving the Schrödinger equation, shows very good agreement. This agreement was improved further by optimizing the parameters used in the numerical simulations [1,3]. This represents a new example where scale relativity theory, based on a fractal space-time concept, can accurately reproduce quantum mechanical results without invoking the Schrödinger equation

A simple phenomenological two-fluid model of nuclear collective motion previously used by the authors to discuss rotations is extended to include surface vibrations.The model is applied to a study of the rare-earth nuclei 154Gd, 164Er and 168Yb in an investigation of the rotation-vibration coupling in the presence of Coriolis antipairing effects and of the effects of Coriolis antipairing in the / I bands.

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The Liouville equation for the q-deformed 1-D classical harmonic oscillator is derived for two definitions of q-deformation. This derivation is achieved by using two different representations for the q-deformed Hamiltonian of this oscillator corresponding to undeformed and deformed phase spaces. The resulting Liouville equation is solved by using the method of characteristics in order to obtain the classical probability distribution function for this system. The 2-D and 3-D behaviors of this function are then investigated using a computer visualization method. The results are compared with those for the classical anharmonic oscillator. This comparison reveals that there are some similarities between these two models, where the results for the q-deformed oscillator exhibit similar whorl shapes that evolve with time as for the anharmonic oscillator. It is concluded that studying the Liouville dynamics gives more details about the physical nature of q-deformation than using the equation of motion method. It is also concluded that this result could have reflections on the interpretation of the quantized version of this q-deformed oscillator.

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