Application of Scale Relativity (ScR) Theory to the Problem of a Particle in a Finite One-Dimensional Square Well (FODSW) Potential

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