q-Dominant and q-recessive matrix solutions for linear quantum systems
- Resource Type
- article
- Authors
- Douglas Anderson; L. M. Moats
- Source
- Electronic Journal of Qualitative Theory of Differential Equations, Vol 2007, Iss 11, Pp 1-29 (2007)
- Subject
- Mathematics
QA1-939
- Language
- English
- ISSN
- 1417-3875
In this study, linear second-order matrix $q$-difference equations are shown to be formally self-adjoint equations with respect to a certain inner product and the associated self-adjoint boundary conditions. A generalized Wronskian is introduced and a Lagrange identity and Abel's formula are established. Two reduction-of-order theorems are given. The analysis and characterization of $q$-dominant and $q$-recessive solutions at infinity are presented, emphasizing the case when the quantum system is disconjugate.