Scholarlink

<p>In this work, we incorporate a weakly <i>q</i>-deformed Heisenberg algebra, characterized by a Generalized Uncertainty Principle (GUP) that implies a minimal measurable length, a minimal momentum uncertainty, and a maximal momentum, into the framework of non-Hermitian quantum mechanics. We apply this deformation to the Swanson Hamiltonian and show that the resulting <i>q</i>-deformed model remains pseudo-Hermitian. Furthermore, we demonstrate that the positive-definite metric operator defining the physical inner product retains exactly the same functional form as in the undeformed case, thereby establishing a structure-preserving incorporation of quantum-gravitational effects. Analytical first-order corrections to the energy eigenvalues and eigenfunctions are derived, confirming the reality of the spectrum and the consistency of the pseudo-Hermitian framework. These results provide a foundation for exploring Planck-scale phenomena in non-Hermitian quantum systems.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Weakly q-deformed operators as a framework for the generalized uncertainty principle in non-Hermitian Hamiltonians

  • 期刊论文

  • 发表日期：

    2026年7月19日

查看全文
  • Linda Ghegal

摘要

In this work, we incorporate a weakly q-deformed Heisenberg algebra, characterized by a Generalized Uncertainty Principle (GUP) that implies a minimal measurable length, a minimal momentum uncertainty, and a maximal momentum, into the framework of non-Hermitian quantum mechanics. We apply this deformation to the Swanson Hamiltonian and show that the resulting q-deformed model remains pseudo-Hermitian. Furthermore, we demonstrate that the positive-definite metric operator defining the physical inner product retains exactly the same functional form as in the undeformed case, thereby establishing a structure-preserving incorporation of quantum-gravitational effects. Analytical first-order corrections to the energy eigenvalues and eigenfunctions are derived, confirming the reality of the spectrum and the consistency of the pseudo-Hermitian framework. These results provide a foundation for exploring Planck-scale phenomena in non-Hermitian quantum systems.