2012/10/25 by P. G. Morrison, Peter G. Morrison, Morrison, Peter G. · 2 citations
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics #quant-ph
paper · pdf · doi:10.48550/arxiv.1210.6977
34 pages, 581 equations
arxiv created 2012/10/25 · openalex publication_date 2012/10/25 · arxiv updated 2012/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained finite systems from this formalism. Once this has been achieved we go on to calculate the wavevector as a function of time, in order to demonstrate the use of matrix methods with respect to several concrete examples. Interesting results are derived for elliptic curves and periodic orbits on higher dimensional non-commutative geometries.