The non-Hermitian operators on the Baker-Hausdorff formula

TL;DR

This paper explores non-Hermitian operators linked to the Baker-Hausdorff formula, focusing on geometric quantum potential and generalized quantum harmonic oscillators, providing new mathematical insights into their structure and relations.

Contribution

It introduces a novel connection between non-Hermitian operators and the Baker-Hausdorff formula in the context of geometric quantum potential and Ri-operators.

Findings

Re-expressed Ri-operator as a more compact quantum formula

Proved new results using the Baker-Hausdorff formula

Clarified conditions for geometric quantum potential

Abstract

This paper provides a connection to the non-Hermitian operators associated with the geometric potential function $s$ and Baker-Hausdorff formula. The geometric quantum potential is considered in a precise condition. The Ri-operator as a non-Hermitian Hamiltonian to describe the generalized quantum harmonic oscillator can be re-expressed as a more compact quantum formula by using the Baker-Hausdorff formula, more deeply, we prove some results based on the application of this formula.