1. Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics
- Author
-
Lan, Chen, Li, Wei, and Geng, Huifang
- Subjects
Quantum Physics ,General Relativity and Quantum Cosmology - Abstract
The spectral collocation method (SCM) exhibits a clear superiority in solving ordinary and partial differential equations compared to conventional techniques, such as finite difference and finite element methods. This makes SCM a powerful tool for addressing the Schr\"odinger-like equations with boundary conditions in physics. However, the Chebyshev differential matrix (CDM), commonly used in SCM to replace the differential operator, is not Hermitian but pseudo-Hermitian. This non-Hermiticity subtly affects the pseudospectra and leads to a loss of completeness in the eigenstates. Consequently, several issues arise with these eigenstates. In this paper, we revisit the non-Hermitian Liouville quantum mechanics by emphasizing the pseudo-Hermiticity of the CDM and explore its expanded models. Furthermore, we demonstrate that the spectral instability can be influenced by the compactification parameter., Comment: 24 pages, 16 figures, typos fixed and references added
- Published
- 2024