2024/05/05 by Shousuke Ohmori, Ohmori, Shousuke
Engineering · Mathematics · #Numerical methods in engineering #Elasticity and Wave Propagation #Algebraic and Geometric Analysis
paper · pdf · doi:10.48550/arxiv.2405.02848
The discussion in this study delves into Dirac's bra-ket formalism for a quasi-Hermitian quantum composite system based on the rigged Hilbert space (RHS). We establish an RHS with a positive definite metric suitable for a quasi-Hermite composite system. The obtained RHS is utilized to construct the bra and ket vectors for the non-Hermite composite system and produce the spectral decomposition of the quasi-Hermitian operator. We show that the symmetric relations regarding quasi-Hermitian operators can be extended to dual spaces, and all descriptions obtained using the bra-ket formalism are completely developed in the dual spaces. Our methodology is applied to a non-Hermitian harmonic oscillator composed of conformal multi-dimensional many-body systems.