Discrete quantum mechanics
- 1 July 1986
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 27 (7) , 1782-1790
- https://doi.org/10.1063/1.527044
Abstract
A discrete model for quantum mechanics is presented. First a discrete phase space S is formed by coupling vertices and edges of a graph. The dynamics is developed by introducing paths or discrete trajectories in S. An amplitude function is used to compute probabilities of quantum events and a discrete Feynman path integral is presented. Many of the results can be formulated in terms of transition probabilities and unitary operators on a Hilbert space l2(S).Keywords
This publication has 10 references indexed in Scilit:
- Discrete quantum theoryFoundations of Physics, 1982
- Finite-dimensional quantum mechanics of a particleInternational Journal of Theoretical Physics, 1981
- Finite-dimensional quantum mechanicsInternational Journal of Theoretical Physics, 1981
- On geometric ideas which lie at the foundation of quantum theoryAdvances in Mathematics, 1979
- Cayley parametrization of semisimple lie groups and its application to physical laws in a (3+1)-dimensional cubic latticeInternational Journal of Theoretical Physics, 1974
- Space-time code. IVPhysical Review D, 1974
- Elementary Length Topologies in PhysicsSIAM Journal on Applied Mathematics, 1968
- Non-Usual Topologies on Space-Time and High-Energy ScatteringJournal of Mathematical Physics, 1967
- The Quantized Complex Space-Time and Quantum Theory of Free Fields. IIJournal of Mathematical Physics, 1966
- Markoff chains, Wiener integrals, and quantum theoryCommunications on Pure and Applied Mathematics, 1952