2006/08/01 by Stefano De Leo, Gisele Ducati, Gisele C. Ducati +2
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Applied mathematics #Classical mechanics #Complex plane #Geometry #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Numerical analysis #Operator (biology) #Physics #Plane (geometry) #Plane wave #Quantum #Quantum and Classical Electrodynamics #Quantum mechanics #Schrödinger equation #math-ph #math.MP
paper · pdf · doi:10.1063/1.2227635
published as J. Math. Phys. 47, 082106-15 (2006) · 15 pages, 2 figures
openalex publication_date 2006/08/01 · arxiv created 2006/09/12 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
By using the recent mathematical tools developed in quaternionic differential operator theory, we solve the Schrödinger equation in the presence of a quaternionic step potential. The analytic solution for the stationary states allows one to explicitly show the qualitative and quantitative differences between this quaternionic quantum dynamical system and its complex counterpart. A brief discussion on reflected and transmitted times, performed by using the stationary phase method, and its implication on the experimental evidence for deviations of standard quantum mechanics is also presented. The analytic solution given in this paper represents a fundamental mathematical tool to find an analytic approximation to the quaternionic barrier problem (up to now solved by numerical method).