2008/06/03 by A. Lavagno · 37 citations
Computer Science · Mathematics · Physics and Astronomy · #Basis (linear algebra) #Commutative property #Geometry #Hermitian matrix #Hilbert space #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Quantum dynamics #Quantum mechanics #Quantum process #Quantum stochastic calculus #Self-adjoint operator #cond-mat.stat-mech #math-ph #math.MP #nucl-th #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/24/244014
published in Journal of Physics A Mathematical and Theoretical 41(24), 244014 (Institute of Physics) · 10 pages
openalex publication_date 2008/06/03 · arxiv created 2008/08/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Starting on the basis of the non-commutative q -differential calculus, we introduce a generalized q -deformed Schrödinger equation. It can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, which reproduces at the equilibrium the well-known q -deformed exponential stationary distribution. In this framework, q -deformed adjoint of an operator and q -Hermitian operator properties occur in a natural way in order to satisfy the basic quantum mechanics assumptions.