Duality between coordinates and wave functions on noncommutative space

2003/09/30 by Ion V. Vancea
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #hep-th

paper · pdf · doi:10.1016/j.physleta.2003.11.049

published as Phys.Lett. A321 (2004) 155-159 · Reference added. 8 pages, LATeX file

arxiv created 2003/10/13 · openalex publication_date 2003/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The relation between coordinates and the solutions of the stationary Schrodinger equation in the noncommutative algebra of functions on R^2N is discussed. We derive this relation for a certain class of wave functions for which the quantum prepotentials depend linearly on the coordinates similarly to the commutative case. Also, the differential equation satisfied by the prepotentials is given.

Citations

• Two kinds of duality
• On the Equivalence Principle of Quantum Mechanics
• Comments on Noncommutative Particle Dynamics
• Star Operation in Quantum Mechanics
• The Non-commutative Landau Problem
• Duality of coordinates and matter fields in curved spacetime
• A Survey of Star Product Geometry